What is the point of calling $\lambda$-calculus an algebra?
A calculus is a system of computation based on the manipulation of symbolic expressions. An algebra is a system of symbolic expressions and relations between them[*]. That is, a calculus is a system for figuring out answers, and an algebra is a way of expressing the relations between terms. 

The $\lambda$-calculus is either a calculus or an algebra, depending on whether you want to think of the $\beta$ and $\eta$ rules as oriented reduction rules or unoriented equations. If you think of the rules as being oriented, then you have fixed an evaluation order, and the rules tell you how to take a term and produce a normal form. If you think of the rules as being unoriented, then they give you the equality relation on $\lambda$-terms.

[*] There is also a categorical definition of algebra, which is a formal definition somewhat more restrictive than the informal idea. Loosely speaking, the difference is that the formal definition of algebra encompasses just those systems without variable binding. So SKI combinators form an algebra, but the $\lambda$-calculus doesn't.