That depends very much on the type of relay you are running.
If you are running a private relay that only you have read and write permissions to, then it's just to keep a backup of your own notes, since other relays may only retain them for a certain amount of time. It also allows you to rebroadcast your notes easily if you are banned from the public relays you are currently using.
If you are running a relay that only you can write to, but anyone else can read from, then you can set this as your Outbox relay, and compatible clients will know to look for your notes on that relay when their users want to see what you've been posting.
It you are running a relay that allows only people within your web-of-trust to post to it, then the benefit would be to greatly minimize the amount of spam you see in your feed, if you are reading from this relay instead of public relays. But it does require that the relay is either importing notes from those in your web-of-trust, or users are actually setting your relay as one they want to write to.
You could also set up a paid relay, and then the benefit to you would be income, while the benefit to other users would be a fast relay with no spam, since spammers don't generally pay.
In other words, there are all sorts of different benefits of running a relay, depending on what sort of relay you want to run.