Kleene algebra is a mathematical structure used to study the properties of regular expressions and automata. It consists of a set of elements, along with operations like addition, multiplication, and a unary operation called star, which represents repetition. These operations allow for the expression of complex patterns and sequences. The key feature of Kleene algebra is its ability to model the behavior of systems that can be described by sequences of actions. It provides a framework for reasoning about the composition and repetition of these actions, making it useful in areas like computer science, particularly in formal language theory and automata theory.