I came across the sum of set, ie $$ A + B = \{\mathbf{a}+\mathbf{b}\,|\,\mathbf{a}\in A,\ \mathbf{b}\in B\}. $$
What does that mean? I can understand unions etc of set, but not the sum.
For example, what is the sum of intervals [0,1] and (2,4)? Or sets {1,2,3} and {0,1}?
It is the set which consists of all the possible sums. The set $A+B$ is called the Minkowski sum of $A$ and $B$. Your examples:
$$[0,1]+(2,4) = \{x+y \mid 0 \leq x \leq 1, \ 2 < y < 4\} = (2,5) \\ \{1,2,3\}+\{0,1\} = \{1+0,1+1,2+0,2+1,3+0,3+1\} = \{1,2,3,4\}.$$