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By definition, none. For if it did have real life applications it would not be called abstract!
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You could consider it as establishing the rules by which the algebra needed to perform real-life tasks works.
For a simple example, if C = AB then you could say, "Fine, suppose we call A and B the sides of rectangle than C is its area, OR if we call A and B speed and time respectively then C is the distance travelled.
In both cases the algebraic rules are the same: multiply two values and you obtain their product; but many practical applications are in fact simple products so there we have the underlying pure algebra for solving them. And from that we can use pure algebra rules to determine A or B from the others.
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