Distinguish between aperçevoir and s’aperçevoir

You are correct about the translation of apercevoir: to glimpse, to see, to take note. The reflexive form, s'apercevoir, refers back to the subject and is used in a more figurative sense. Apercevoir is to see something, while s'apercevoir is more like "to become aware" of something. Think of it as seeing with one's mind.

Jean aperçoit son amie dans la foule. -- Jean glimpsed his friend in the crowd.
Jean s'est aperçu qu'il avait perdu ses clés. -- Jean realized that he had lost his keys.