To be seeing someone

If you're seeing someone, it means that you're dating. It may mean more or less involvement, depending on the situation, but it always means that you're spending time with the person in a romantic way. Here are a couple of examples:

Him: Would you like to have dinner with me on Saturday?
Her: Um, actually, I'm seeing someone.
Him: Oh.
*******
Her: He seemed pretty disappointed when I told him I was seeing someone.
Her friend: Yeah, I bet he was. But are you really serious about Felix?
Her: Well, we've been seeing each other for a while now, but I'm not sure...
*******
As you can see, we usually encounter this phrasal verb in the continuous, and we don't usually use it in the future. So we would say "He was surprised that she was seeing someone," to express a situation in the past.