There are multiple meanings for "see (someone". One is to simply see someone with your eyes:

I saw her at the farmer's market yesterday.

But you can also use the phrase "seeing someone" to mean "dating". For example, if you're interested in a person you can ask:

Are you seeing anyone?

This means, "Do you have a boyfriend / girlfriend?"

I'd like to see you again sometime.

This means "I'd like to go on another date with you."

The expressions using "see" sound cooler and more natural than directly using words like "date", "boyfriend", "girlfriend", and so on.