Eigenvectors: Eigenvectors are basically used to understand linear transformations. These are calculated for a correlation or a covariance matrix.
For definition purposes, you can say that Eigenvectors are the directions along which a specific linear transformation acts either by flipping, compressing or stretching.
Eigenvalue: Eigenvalues can be referred to as the strength of the transformation or the factor by which the compression occurs in the direction of eigenvectors.