For example, in the rule A→Xα, X is the left corner.
The left corner table associates a symbol with all possible left corners for that symbol, and the left corners of those symbols, etc.
Given the grammar
|S||VP, NP, V, DET|
Left corners are used to add bottom-up filtering of a top-down parser.
You can use the left corners to do top-down filtering of a bottom-up parser.