The other answers indicate that Trump has appointed an unusually large number of judges, but they don't quite get to how Trump was able to nominate so many more judges than previous presidents.
Vox: What Trump has done to the courts, explained
One reason is that the Senate under the final two years of Obama's term was controlled by Republicans, and under their majority, they worked to keep federal judicial vacancies open for as long as possible.
The first reason is the effective blockade Senate Majority Leader Mitch McConnell imposed on appellate court confirmations the moment Republicans took over the Senate. McConnell’s effort to block Supreme Court nominee Merrick Garland is well-known. Less well-known are the many lower court nominees who received similar treatment. Under Trump, McConnell’s turned the Senate into a machine that churns out judicial confirmations and does little else — he’s ignored literally hundreds of bills passed by the House. Under Obama, by contrast, McConnell’s Senate was the place where judicial nominations went to die.
The numbers here speak for themselves. In the final two years of the Obama presidency, when Republicans controlled the Senate, Obama successfully appointed only two federal appellate judges — and one of those judges, Kara Farnandez Stoll, was confirmed to a highly specialized court that primarily deals with patent law.
By contrast, 10 such judges were confirmed during the same period in the George W. Bush presidency — a period when Democrats controlled the Senate.
This was compounded by the prior Democratic majority's attempt at maintaining a degree of bipartisanship in the Senate. Senator Leahy did not want to take away the power of minority Senators, and in doing so, he allowed them to hold some judgeships open for almost the entirety of Obama's term in office.
The second reason for Trump’s outsized impact on the judiciary is that, when Democrats last controlled the Senate, one especially important Democrat — Judiciary Chair Patrick Leahy (VT) — took an unusually expansive view of the rights of the minority party.
An informal tradition known as the “blue slip” sometimes gives home-state senators an exaggerated influence over who gets confirmed to federal judgeships within their states (the tradition gets its name from blue pieces of paper that home-state senators use to indicate whether they approve of a particular nominee).
Traditionally, the Senate Judiciary Committee showed some level of deference to senators who disapprove of their home-state nominees, although the level of deference given to these senators varied wildly depending on who chaired the committee and whether that committee chair was politically aligned with the incumbent president.
Leahy, who chaired the Committee for most of the Obama presidency, gave home-state senators a simply extraordinary power to block judicial nominees. Under Leahy, a single senator of either party could veto any nominee to a federal judgeship in their state (although federal appeals courts typically oversee multiple states, each individual seat on these courts is traditionally assigned to a particular state).
New York Times: (Opinion) The Left Shouldn’t Freak Out About Trump’s Judges (Yet)
This opinion piece in the New York Times supports the same conclusion.
Why is President Trump filling so many vacancies? Because Republicans stalled Obama nominees and then abandoned the custom of deferring to the wishes of home state senators, which would have blocked or modified Trump nominees in blue states.
The Fifth Circuit is a prime example. That court, which covers Texas, Louisiana and Mississippi, has leaned right for three decades largely because Texas’ Republican senators blocked all but one actual or potential Democratic appointees from that state since 1995, and Presidents Bill Clinton and Obama let them get away with it. Unlike Mitch McConnell, Harry Reid, the Democratic Senate majority leader, was too wedded to Senate tradition to challenge the traditional veto enjoyed by home state senators, and the seats remained empty until 2017.
