The other responses are correct, but they left out one important thing. People like to feel important. People like to go places other people can't. People get off on exclusivity. If you have an empty field no one will care. You put a big wall up and signs saying keep out all of a sudden people will risk their life climbing the wall just to get to that empty field. It's human nature.

Most likely for lobbying purposes. You might want to support or block a bill, resolve an issue that affects you, or push for legal changes or permits that benefit your business. It's about influencing decisions that have a direct impact on your interests. And it doesn't even need to be business related; sometimes it's just like calling the building manager when something is annoying you and you're bored.

The other answers are practical (e.g. lobbying) but I’ll give a less practical angle: proximity to uniqueness and power.

There are only 100 U.S. senators at a time. In contrast, Forbes estimates there are about 900 billionaires in the U.S. alone this year.

And it is extremely difficult to become a Senator. Many very rich people have tried and failed to win election to the U.S. Senate. It’s not as straight forward as success in business. Politics is somewhat like magic. It’s extremely difficult to predict what is going to attract votes when. A lot of very confident rich people have been humbled this way.

Politicians are also demonstrably popular in ways the very rich are not. You only become a Senator if hundreds of thousands, to millions, of individual citizens vote for you (depending on the state). Congress overall is unpopular, but individual politicians are fairly popular to their own constituencies. Again, this is not something you can just buy, and many very rich people are thirsty for this kind of public validation.

Finally, Senators have real power, at least collectively. If enough Senators agree on something, the police will make you do it. Rich people want to shape those decisions if they can, yes, but many also like the feeling of being “close” to that kind of power. Since most will never have it themselves.

The above goes for the president even more. And for many state governors too.

Generally for the influence it can give them. If you don’t like how something is happening if your city/state/country, talking to those people can give you the power to get it changed.

Having friends in high places can also help if you happen to run into legal issues. Though there is growing scrutiny around this.

The rich and powerful businessmen in your country are doing it too with the politicians in your country to have favourable laws for them.