A Banach algebra is a type of algebraic structure that combines the properties of a normed space and an algebra. It consists of a set of elements where you can perform addition, multiplication, and scalar multiplication, while also having a way to measure the "size" of elements through a norm. This norm must satisfy certain conditions, making the space complete, meaning that every Cauchy sequence converges within the space. In a Banach algebra, the multiplication operation is associative and distributive over addition. Additionally, it often includes an identity element, which acts like a multiplicative "1." These structures are important in functional analysis and have applications in various fields, including quantum mechanics and signal processing.