READ THE HELP. Ok, it may be proper here to tell you to take a linear algebra course if you do not understand LU decompositions or eigenvalues and eigenvectors. There are entire books written on these subjects, so do you really expect us to do better here, off the cuff?
From the help for lu:
[L,U,P] = lu(A) returns unit lower triangular matrix L, upper
triangular matrix U, and permutation matrix P so that P*A = L*U.
So L is a lower triangular matrix. It has the property of having a unit diagonal.
U is an upper triangular matrix.
P is a permutation matrix, that essentially does pivoting to make the problem well-posed, thus avoiding zero pivots.
If you really need more than this, for example, what a matrix factorization is or why one would build it in the first place, then you REALLY need to learn some (numerical) linear algebra. Almost any basic text will cover this in great detail.
