Hey Becky!
A short explanation based on most common use.
Not considering all definitions you can find looking up on a dictionary, but only common speech.
Perceber - understand
"Aperceber- se" - being aware or realizing something. To acknowledge or note something you didn't until a given moment.
An example about this exact situation:
Tu consegues perceber português mas quando estás a estudar português apercebes-te das diferenças entre o português do Brasil e o português de Portugal!