Cech cohomology is a mathematical tool used in algebraic topology to study the properties of topological spaces. It involves covering a space with open sets and examining the relationships between these sets to derive cohomology groups, which provide insights into the space's structure and features. This method is named after the mathematician Eduard Čech, who developed it in the 1930s. Cech cohomology is particularly useful for spaces that may not be well-behaved, allowing mathematicians to analyze complex topological properties through a systematic approach involving sheaves and cochains.