A term used in the seduction community. Approach invitation is best defined as a sign that a woman is interested in a man, and she wants him to approach her. Approach invitations come in many ways. They include prolonged eye contact, being unnecessary close to the man in particular, unnecessary hair touching/tossing, loud talking/laughing when near. In other words, the woman is trying to get his attention in a subtle, or not so subtle way. Approach invitations don't last forever though, the woman might get frustrated when her invitation is ignored after a short amount of time, and she will give up. The man needs to recognize these signs and approach her fast.
"James, stop standing against the bar like a police officer! Can't you see that HB over there that keeps glancing over to you and tossing her hair like crazy. She's giving you a massive approach invitation. Go talk to her and make her happy while you still can, you blind idiot."