Each time I see a press conference where President Trump is there, the reporters ask questions and he always answers them. Is he forced to do so by any law or something, or does the President just answer because it is part of democracy?
He is not obliged to hold them at all, much less answer questions, or any specific questions.
The only requirement of addressing anyone is the state of the union, and that is not required to be a speech, it could be written.
He shall from time to time give to the Congress information of the state of the union...
That same section also says he has to receive ambassadors and other public ministers, but says nothing about answering questions there either.
There is no constitutional oblication, but it is an axiom of a democratic system that a president who wants to achieve his or her political aims must do so by persuasion.
A president in a democracy who refused to meet the press and answer their questions would be neglecting one of the chief advantages of their position. By holding press conferences the president can tell people about his or her policies and present arguments for supporting them. The president can also use the forum to (verbally) attack their opponents. Presidents use this to build a coalition of support, both in the Legislature and the country. The two go together, as Senators and Representatives are much more likely to support a proposal that is popular.
Now there are other ways to get your message across, but meeting the press is an effective one. If you just published your own messages people will ignore them. They are much more interested in seeing the President defend his or her policies and will watch news programs, or buy newspapers but not watch a political advert.
So the president has to deal with the press and answer their questions to get on the news programs and so get his or her message across.
There is no constitutional imperative. But all Presidents do need to meet the press if they want to be successful.
The other answers are overlooking a fairly obvious point. While there is no requirement for a President to hold press conferences, or to answer press questions, most if not all Presidents in the past century have done so. (The first formal press conference seems to have been held in 1913, during the Wilson administration: https://www.whitehousehistory.org/press-room/press-timelines/the-white-house-and-the-press-timeline ) Most Presidents have apparently thought that it was a good idea to keep the public informed.
However, you may have noticed that press conferences under the current administration are rather different than in previous ones. The current incumbent apparently likes to hear himself talk. His "answers" to questions are often not responsive, and reportedly* descend into attacks on the reporter asking the question, or their employer.
*I say reportedly, since I have other things to do with my time rather than watch press conferences. However, a search for "president attacks reporter at press conference" returns in excess of 29 million hits.