Imagine a piano. The distance from B to C is a half step because no other notes fall between them. The distance from A to B, however, is a whole step because it consists of two half steps.
Each note is a certain distance apart from the next, and they form a pattern that repeats. There are two naturally occuring half steps. In the key of C Major, those two half steps are between B & C and E & F.
Accidentals raise or lower notes by half steps.
# - sharp - raises the pitch 1 half step
b - flat - lowers the pitch 1 half step
The interval between E and F is a naturally occuring half step, but if we raised F to F#, we then make the distance further apart. The distance between E and F# is now a whole step because it consists of two half steps (E to F and F to F#).
Several notes share the same pitch but have different names. For example, A flat is the same pitch as G sharp, and C sharp is the same pitch as D flat. Typically, you would call the half step between C and D a C sharp if there is a C sharp in the key signature or a D flat if there is a D flat in the key signature.