It might be more useful if you actually had to look at someone's profile to click on "Meet Me", but as it is, they're just saying they like your photo. I stopped responding after the first few women who clicked "Meet Me" on my profile never replied. It's pretty useless feature, especially on a free dating site.
I have not been on this site long and wondered if the Meet me thing was fake or system generated and that now appears to be somewhat true. Because of my background (geek) , I am not going to appeal to too many women and figured something was up with all those Meet me messages. Thanks for clearing this up.