White Stuff Around eye?

Hey,

My neighbor just gave me a dog whom she was going to put asleep. Well, she told me that white stuff usually builds up in the middle of his eye and that I'd have to wipe it off. So...I have no idea what the hell this is. She didn't tell me exactly what it was either. So I'm sitting playing some video games when my dog starts growling while he's on his back swerving from side to side and I can see the white stuff build up.

I thought this was a seizure at first because I've never seen a dog do this. She gave me his papers; they're pretty old so the ink was faded and it was almost un-readable. But on the "breed" line, I think it read Maltese. He's black and brown. Umm...could it be the hair covering his eyes that's doing this? I just want to know what this is and see how I can rid of it.