Impeachment hasn't substantially improved Trump's approval rating.
Approval rating fluctuates for every president, as it's based on (a tiny subset of) the people's opinion, so you have to get the average of not only multiple polls, but also across multiple measurements in time, to see if it's actually trending up and trending down.
This is the historic trend of Trump's approval rating (black line) and disapproval (red line), over the past two years.
Here's me roughly averaging it his approval polling, by eyeballing it (blue line).
Here's me adding in the start and end of the Russian investigations, and the start of the Ukraine scandal and impeachment:
When you look at the broad picture, you notice that as he got ensnared in the Russian investigation and continued criticism and bad press over treatment of illegal immigrants, he dropped in approval, but it has since balanced out and has mostly held steady over the past year-and-a-half, with a small gradual upward trend as the economy has continued to do well. By "holding steady", it still has the regular up and down bouncing of people's opinions in the average of a dozen tiny polls measuring a thousand people here, a thousand people there, out of a nation of >325 million.
Trump's gradual upward trend pre-dates the impeachment process, by over a year.
Further, the fluctuations are of a few tiny points here or there, e.g. 1 out of a hundred people changing their mind slightly from "Extreme disapproval" to "Mild disapproval" or from "Neutral" to "Mild approval". These are not big swings of the population, if you look at the scale on the left side of the chart.
The impeachment hearings were rushed through so quickly, that it's really too short of a polling period to filter out the regular fluctuations of Trump's approval from the effect of the impeachment.
The impeachment hasn't had a substantially noticeable impact one way or another, with the exception of a small blip right when it began.
In my interpretation of this data, I'd say that it's not that the impeachment has increased Trump's approval, it's rather that the impeachment hasn't substantially decreased Trump's already very-very-very slowly increasing approval trend that started over a year prior to impeachment.
That much I can discern by looking at the raw polling data. So, the question becomes not, "Why has impeachment helped Trump?" (which it doesn't seem to have - at least, not enough evidence exists to substantiate that), but rather "Why hasn't the impeachment hurt Trump?".
To answer that new question, we have to enter speculation, which obviously gets distorted by our personal biases.
Why hasn't the impeachment hasn't decreased Trump's approval? [Speculation / Personal opinion]
Any change in the polling we're measuring are mostly people who are neither concretely locked into being pro-Trump (concreted pro-Trumpers are solidly 38% of the country who've supported him without fluctuating) nor people concretely anti-Trump (solidly 42% of the country who haven't wavered against opposing him).
I would speculate, based on my biased interpretations of the trends visible in the charts above, that voters that are neither permanently Pro-Trump nor permanently Anti-Trump were really bothered by, and concerned about, Russian interference, and that the Russian investigation hurt Trump with these voters. The national narrative was, "Trump himself explicitly colluded with the Russians to win the election, and is working to impede the investigation."
But after the Russian investigation ended there was little concrete evidence that Trump colluded with the Russians (though he did impede the investigation in my opinion, but Mueller refused to issue a "verdict" on that), and non-concreted Americans mostly thought Trump was vindicated on the primary charge: outright collusion with Russia.
Then, when the Ukraine scandal began just a month or two later after the Russian investigation ""cleared"" Trump (or at least didn't convict him badly enough to be impeached), to these independents, it possibly failed to work against Trump, for several reasons:
First, to some, it looked like Democrats failed to convict him on outright
collusion with Russia, and now were just throwing something else at
him to try to get him out of office.
Second, what they were now impeaching him over ("clumsily abusing his office
to get an edge over Biden in re-election") pales dramatically in
comparison to "treason against the United States by colluding with our
Third, Joe Biden has terrible optics here. Biden is on video openly bragging about removing a Ukraine investigator investigating a Ukraine company that his son, with zero relevant experience, was getting paid $600,000 a year by. (This was not Biden's motivation, and is missing nuance that vindicates Biden, but that's the narrative many were hearing). It doesn't help that Biden publicly stated he never discussed his son's Ukraine work, followed by Trump's campaign releasing photos of Joe Biden with his son and his son's Ukrainian boss golfing together, and these photos went viral. Trump putting
pressure on Ukraine to reopen that investigation can, by squinting in
the right light, be seen as almost reasonable to independent voters.
Independents here aren't sympathetic to Biden, as it looks very "swamp-like" on the surface.
Fourth, the Russian investigation went on for months and months and
months, and seemed really official and thorough, and was conducted
independently by FBI, at the request of congress. In contrast, the Ukraine
impeachment sped by in just two months, entirely controlled by a single
political party, and the voting was entirely along partisan lines. No matter
how neutral, fair, or unbiased they may have been, the optics looked partisan
as hell in comparison to the Russian investigation.
Fifth, Trump's phone call that was the focus of the impeachment is
rather ambiguously worded. In typical Trump fashion, he rambled around non-stop, jumping between multiple topics. To impassive third parties, it just sounds like clumsy Trump speaking clumsily. The reasoning goes, Trump is like a bull in a china shop, and if he was trying to do quid-pro-quo, he likely wouldn't have been subtle.
Sixth, the Prime Minister of Ukraine, who the articles of impeachment
claims was being "pressured" by Trump in a quid-pro-quo, openly
claims he wasn't being pressured, and it wasn't a quid-pro-quo. Sure, he could just be not wanting to rock the diplomatic boat, or even trying to win favor with Trump, but him publicly saying that does harm the perception of the impeachment process to undecided voters.
Seventh, several expert Democrat witnesses the Republicans had provided to testify during the impeachment process - professors of law at various universities - very smoothly and publicly articulated why they opposed the impeachment, and why they, as Democrats, thought the Democrats were in the wrong. Accurate or not, that harms the optics of the impeachment process.
(Note: I keep using the word "optics", because we're talking about why public polling of random citizens many shift one way or another. In such cases, optics is everything, as unsubstantiated opinion is exactly what the polls are measuring).
Eighth, it's come out recently that the CIA made several huge mistakes during the past Russian investigation, that cast the Russian investigation in a bad light, and make the Russian investigation look more partisan in hind-sight. These revelations occurred during the impeachment process, and their effect on the polled public's perceptions can't be separated from the effect of the impeachment hearings themselves. For example, James Comey himself has been publicly admitting he botched part of it, when getting the FISA warrants to even begin the investigation.
And finally, a few Democrat congressmen have openly said they need to impeach Trump so he doesn't win re-election. Giving the impression that the impeachment is just a partisan attempt to derail Trump, in the same way they are claiming Trump was abusing powers of office to derail Biden. Sure, hundreds of Democrats may have been taking the impeachment process in a perfectly unbiased and neutral way, but if even one or two Democrats publicly say they themselves are being partisan, it gives the impression all the two hundred others silently are also.
All this adds up so that people who are neither rabid anti-Trump nor rapid pro-Trump could feel far less worried about the Ukraine scandal than they did about the Russian scandal, and isn't letting it tamper their slightly rising approval over the good economy.
Note: As the question itself is one that can only be answered by speculating individual voters opinions, I've tried to provide reasons why they might have leaned more Trump-ward over the impeachment process.
No concrete answer can be given without examining the unique individual minds of the voters polled.