"Locking eyes" is the Romantic's term for "staring intensely" or "losing yourself" while staring into another person's eyes. It indicates that you've been captured by the person's stare and are having a hard time looking away. It's a sign that you're into the person -- and that they're into you.
In business meetings it's a sign that the other person is trying to read/intimidate you. In romance it's a sign that the person is trying to read or understand something about you. In both cases they're often looking for a "tell" of what you'll allow...and what they can get away with, lol.
She's into you. The fact that you look looked back at her tells you that you liked the attention, though it made you uncomfortable at first. Something like that happened to me once and I'd look down at my hands or his tie, but when I looked back up he'd still be staring, sort of grinning, stoking the flames with his eyes. ;-)
Enjoy the moment for what it is. It doesn't necessarily have to amount to anything.
I have the same thing happen to a guy I like. When I stared into his eyes and he looked into mine, I felt so comfortable and it was like me and him were the only 2 people in the whole room. It felt right. I asked people what they thought it meant and a majority of them said that he probably likes me back. Since she stared at you a lot, seems to me she likes you :)
Yes it does mean something I done correctly. Many men whimp out when thy make eye contact with a girl, it scares them. For women, if you're a man and you make eye contact with her and you hold it, it shows confidence. Eye contact is exceptionally powerful when done correctly. If she holds it and doesn't look away, she's interested. I always tell guys to make it a habit not to look away, as uncomfortable as it may feel. Locking eyes with a woman and you two staring at each other deeply is very powerful. Beware of the stalker/creeper look if your a guy though haha.