Translation:We do not forget our birthday.
According to two dictinaries I have consulted so far (italian app linked to wiktionary.org and Dizionario Italiano app by The free dictionay.com), the word "compleanno" comes to Italian feom the Spanish "cumpleaño". In Spanish "cumpleaño" is used to refer not only the birthday (date) but also the birthday party.
I did not find any information to sustain this interpretation or translation bit it might be referring to the party.
Equally in English the word birthday can refer to the festivity or party. Even though it is more likely to hear "birthday party".