What a data structure is, in short
A data structure is a way of organising data in memory so that certain operations, such as looking something up, adding or removing it, are efficient. Choosing one is a trade-off: a structure that makes lookups instant may make insertions slow, or use more memory.
Niklaus Wirth summed up their importance in the title of his 1976 book: Algorithms + Data Structures = Programs.
Same items in, different item out
Add items to both, then remove one. A stack gives back the newest (last in, first out); a queue gives back the oldest (first in, first out).
Jump straight to the right drawer
A hash function turns a key into a bucket number, so you can find it without searching. Ours adds up the letter codes and takes the remainder after dividing by 8. Add names and watch for collisions.
Left is smaller, right is bigger
In a binary search tree, every node's left branch holds smaller values and its right branch bigger ones. Each comparison throws away half of what's left. Pick a value to find.