What is an algebra for an algebraic theory?

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Definition 1.1 of Algebraic Theories says an algebraic theory is a small category $\mathcal{T}$ with finite products, and an algebra for theory $\mathcal{T}$ is a product preserving functor $A$ from $\mathcal{T}$ to $\text{Set}.$

My question is, how is this concept related to the idea of an algebra over an endofunctor or of an algebra over a monad ?

For example, I am wondering if there is a connection with some Eilenberg-Moore categories.