Via Wikipedia https://en.wikipedia.org/wiki/Exterior_algebra#Differential_geometry, there is this given definition
"In particular, the exterior derivative gives the exterior algebra of differential forms on a manifold the structure of a differential algebra."
What does it mean? How does this give the exterior algebra of differential forms on a manifold the structure of a differential algebra?
On
A differential algebra is an algebra (a vector space with a vector-valued product defined between any two vectors) equipped with a derivative (a function from vectors to vectors that is linear and satisfies the Leibniz product rule with respect to the product of the algebra).
In the exterior algebra of differential forms on a manifold, the vectors are differential forms, the product of the algebra is the exterior product, and the derivative is the exterior derivative. These operations satisfy all the requirements in the definition of a differential algebra.
The set of differential forms along with addition, scalar multiplication, and the exterior product is an algebra (over a field). Add the exterior derivative and you get a differential algebra. That is, an algebra with an operation which is linear and obeys Leibniz's rule.