Understanding the Addition of Subspaces in Linear Algebra

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What exactly is the "addition of subspaces?" It is obviously not the same as the "union of subspaces," since the union of subspaces A and B in V is a subspace of V only if A is contained in B (or B is contained in A).
 
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You should probably only ask the same question in one place.
 
It probably refers to the direct sum of two vector spaces. Link.
 

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