A spectral sequence is a mathematical tool used in algebraic topology and homological algebra to study complex structures. It provides a systematic way to compute homology or cohomology groups by organizing information into a sequence of pages, each containing a series of abelian groups and differentials that relate them. The process involves starting with an initial page and applying a series of operations to derive subsequent pages. This method can simplify calculations by breaking down complicated problems into more manageable parts, making it easier to understand the relationships between various algebraic objects, such as chain complexes and cohomology theories.