Think of it like this: say you're at work and have an important meeting in a few days. If you're anything like me, your mind will constantly return to it. You play out scenarios in your head about how it will go. If you're a natural pessimist, you can imagine all sorts of failure modes.
So let's say your normal response is to spend ten seconds of fantasy, in which time your heartbeat rises, stress hormones begin circulating in your blood, muscles clench. You may even mutter to yourself.
So then, you meditate. It's a bit like training yourself to spot when your mind wanders. Now you only drift into useless fantasies for five seconds before you catch it and bring yourself back to the present. Only half the hormones enter your blood. Your heart rate is lower. Your stress is less.
Anyway, that's one benefit I've found.
There are others, too. Many studies have found that the key to creativity lies in taking a break from work and letting the mind relax. Well, I often find I get my best ideas during a meditation session. Like all other ideas, I try to bring my mind back to the present and ignore them, but after the session, they're still there for me to use.
I could get into the spiritual side, too. You don't need to believe in a god to see that there's times when you feel more connected to other people and to nature. I don't know why, particularly, but meditation seems to make this happen more often. Speaking for myself only, it's a very pleasant feeling.