What is the point of censuring them? Is there any tangible effect of them doing this? Or is it just a stronger version of saying that they did a bad thing?
TL;DR: they call for a censure vote to embarrass their political opponents and gain political advantage in the next election.
There are no official ramifications of a presidential censure. The targets may happily go about their lives afterward.
There are some political effects of a censure vote or a failure to vote on a censure. If there is not a censure vote on Donald Trump, then Democrats can accuse Republicans of blocking the censure. If there is a roll call censure vote, then there is a record of it. Voting in either direction can be problematic. A Republican who votes against censure of Trump can have that fact used in political advertising. A Republican who votes for censure might lose a primary election. Or they might find ways to highlight that vote, which will tend to depress Republican turnout.
I'm talking about Trump because that's the current situation in the news. But the same principle applies to any president of either party. And the same effect shows up in other issues besides censure votes.
We could see a similar effect in elections in 2016. Joe Heck opposed Trump. Both Trump and Heck lost the state of Nevada, Heck quite narrowly.
Also, only three Democrats of thirty-four who voted against Obamacare are still in Congress. That's more than half the total drop of fifty-nine seats from 2010 to 2015. Voting against one's party is as dangerous as voting with it. In many ways more. Over a hundred Democrats voted for Obamacare and are still in office. Of course, the Democrats still in office who voted for Obamacare are mostly in safer seats than those who lost.
Anyway, the point here is that a censure vote on Trump hurts Republicans more than Democrats. Most if not all Democrats can safely vote against Trump. A number of Republicans have no good response. They may lose independent votes if they vote no. And they may lose Republican votes if they vote yes. But partisanship means that they won't gain many votes by voting yes.