Non-deterministic finite automaton-transition function

Question

When we define:
$δ:(Q \timesΣ\to2^Q)$
$2^Q$ represents the numbers of transitions or the resulting position after the automaton get letter?

Answer 1

$2^Q$ encodes the subset of $Q$ that are active after evaluating the input string. If there are states $Q_1, Q_2, Q_3, ...$ then examples of elements of $2^Q$ are $<yes, no, yes, yes, no,...>$ which can also be written $<1, 0, 1, 1, 0,...>$ where $yes$ or $1$ represents that state being active after the string is evaluated.