I am wondering why fast matrix multiplication are impractical, especially for boolean matrix multiplication.

I read some contents saying fast matrix multiplication are impractical because of large constant factor. These constant factors are because of algebraic techniques. I do not understand where these constant factors come from. Some references also say $O(n^{3-\omega})$ may become practical when $O(n^{3-\omega})$ combinatorial algorithm exists. I want to know what the large constant factor and combinatorial algorithm for boolean matrix multiplication is.