cumplir
Cumplir means to fulfil — which covers birthdays, promises, rules and sentences. English uses a different verb for each.
cumplir (age)
To turn a given age. The verb for birthdays.
Cumplo treinta años el lunes.
I turn thirty on Monday.
Cumplir + age. The number plus 'años' is the object.
¿Cuántos años cumples?
How old are you turning?
Asked about the coming birthday. 'Cuántos años tienes' is how old you are.
Mi hija cumplió cinco años ayer.
My daughter turned five yesterday.
The birthday that just passed.
cumplir (fulfil)
To do what's required — a promise, rule, deadline, sentence.
Siempre cumple sus promesas.
He always keeps his promises.
Cumplir una promesa = to keep a promise. 'Mantener' is rarer.
Hay que cumplir las normas.
You have to follow the rules.
Complying with rules and regulations.
Cumplió condena de tres años.
He served a three-year sentence.
Cumplir condena = to serve a sentence.
Tricky bit
'Cumplir con' is used for duties: 'cumplir con su deber' = to do one's duty. Without 'con' you get a direct object ('cumplió su deber'). Both are fine, but 'con' is more common for abstract obligations.