In my lecture notes, the following text appears:

"..We know that if $(X,d)$ is a metric space and $\mathbb K$ is $\mathbb R$ or $\mathbb C$, then $C(X,\mathbb K)$, that is the space of continuous function from $X$ to $\mathbb K$, equipped with the norm of uniform convergence, is a unitary algebra.."

I never came across the term algebra.

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> What does an "algebra" mean in this context? And what does "unitary algebra" mean? 
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Don't bother yourself with a thorough explanation or something, I just need an $a$$b$$c$$d$.. list of the conditions that must be satisfied by a space of functions to be called an algebra, and what is the additional condition that makes it a unitary one. I know that the term "algebra" should not merely be a description for certain function spaces, it should describe a general vector space under certain conditions; but currently, I am just interested in what it means in this context and how the conditions are expressed in terms of functions for the purpose of direct application. 

Additionally:

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> When is a subspace called a "subalgebra"?
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Again, I can relate to similar terms containing "sub" to guess that a subspace is called a subalgebra if it is an algebra by its own (with the induced operations from the initial space); but I need an $a$$b$$c$$d$.. list of what makes a subspace a subalgebra.

Thank you very much.