The Six Fundamental Logic Gates
Every digital circuit, no matter how complex, decomposes into combinations of a small set of fundamental logic gates. AND outputs true only when both inputs are true; OR outputs true when at least one input is true; NOT inverts a single input; XOR outputs true only when the inputs differ; NAND and NOR are the negated (inverted-output) versions of AND and OR respectively.
NAND and NOR deserve special mention: either one alone is "functionally complete," meaning any boolean function whatsoever — including AND, OR, and NOT themselves — can be built using only NAND gates (or only NOR gates). This is why NAND is often the actual gate physically fabricated on silicon, with other gate behaviors synthesized from combinations of it, rather than manufacturing six different physical gate types.
Toggling inputs and watching the output update in real time is a faster way to build intuition for gate behavior than reading a truth table cold, especially for the less intuitive gates like XOR and NAND.