You're a single guy. You met a girl at your friend's party and hit it off with her. Now your friend is asking what you think of her. You would like to go on a date with her. You say:
I wouldn't mind seeing her again.
You use the phrase "I wouldn't mind ___ing" when you want to do something, but you don't want to seem too eager. In the example above, even if the speaker is really interested in this girl and excited about seeing her again, he probably wants to act cool in front of his friend.
To "not mind" something means to be OK with it, or to not be bothered by it.
You can 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.
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