This means to show that you notice someone, by talking to them, smiling at them, or just making eye contact (which is when you both look at each other's eyes).
More generally, to "acknowledge (something)" means to admit it, or to show that you notice and recognize it. For example:
Don't you think that his mother should at least acknowledge me? That's just rude.
The U.N. said it had asked North Korea for a meeting about all of this, but the North Koreans even refused to acknowledge that they had received that request for a meeting.