The difference in meaning is very little, but grammatically those are two different forms.
"Olvidar" is a transitive verb, it needs a direct object. Ex: Olvidé las llaves, olvidé el paraguas, no olvides abrigarte, olvidaste preguntar.
"Olvidarse" in an intransitive verb, it needs the preposition "de", it's often used when in forgetting to do things, but it can be used in any context.
Ex.
(yo) me olvidé de su número de teléfono.
(ella) se olvidó de cerrar la puerta.
It can also be used as intransitive in 3rd person.
Se me olvidaron las llaves.
Who forgot the keys? - me. (then 'me' refers to me, indirect object)
what did I forget? - the keys. (then 'se' refers to the keys, direct object)
conclusion
Yo olvidé las llaves = Se me olvidaron las llaves (means the same, but different structures)
In a conversation I can ask you.
¿Olvidaste las llaves?
- Sí, se me olvidaron (what? the keys, cause you're already talking about that)
I hope it helps. You can contact me if you need something else :)