"I see" can be understood as "I see what you mean". It's a figurative use of "see", and yes it means "I understand".

They're very close to each other. Understand means comprehend, "I see" means I realise why. But they are very close, it's not so easy to give a proper, detailed explanation of the difference. If someone explained a mathematical problem to you, or they said why you should not go to a meeting or something like a funeral, you would say: "I understand" (it makes sense, it's rational/reasonable). If someone says something like: "you can't go in that part of the building because you don't have the right key code", you'd say "I see!" (it's realised). Check out the brass balls on that hehehe

It means "I understand". People use it when someone is explaining something to them or telling a story and the listener wants to show that they are paying attention and following the story.

i see means i understand