A singular matrix is a square matrix that does not have an inverse. This occurs when the determinant of the matrix is zero, indicating that the rows or columns are linearly dependent. In simpler terms, at least one row or column can be expressed as a combination of others, which means the matrix cannot span the entire space. Singular matrices are important in various fields, including linear algebra and computer science. They can arise in systems of equations where there are either too many equations or not enough independent information, leading to no unique solution.