"The Eye" is an body expression that is usually used in a topic about girls. "The Eye" is when a girl's eye dilates ( The pupil gets bigger ). When this happens this means the girl sees something she likes.
Here is an example from a song by Common called "Punch, Drunk, Love." feat Kayne West.
" Hey baby am I crazy or was you giving me the eye? You said maybe, well you crazy because I know I'm too fly... "
The Eye is one of three main parts that together make what is called "The Cyclops". For its definition see Cyclops.
The Eye is a glass bowl that connects to the top of The Cyclops. Crystal meth is placed inside The Eye, where it is heated then smoked.
The glass bowls position on top and the hole in its side. Where crystal is added and during it's use a plug is inserted to regulate airflow, resembles the eye of a mythical creature called Cyclops.
"Hey can ya pass over The Eye for us thanks, but watch out it's fucken hot"