Informally: imagine a sack that contains a whole lot of bags of marbles. You can take the marbles out of their various bags and fill the sack directly with them. (I don't know why set theory can't be more visual.)

Formally: **A**x **E**u **A**a (a **in** u <=> **E**b (a **in** b & b **in** x))

The new set u is called the union of x, and is denoted **U**x (actually with an extra-large union symbol U). The more familiar notion of a union of two sets, denoted A U B, is the particular case **U**{A, B}.