die Geburtstagsfeier
birthday party
A celebration or party held for someone's birthday.
Wir organisieren für Oma eine große Geburtstagsfeier mit der ganzen Familie.
We're organizing a big birthday party for Grandma with the whole family.

birthday party
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birthday party
A celebration or party held for someone's birthday.
Wir organisieren für Oma eine große Geburtstagsfeier mit der ganzen Familie.
We're organizing a big birthday party for Grandma with the whole family.

The word consists of 'Geburtstag' (birthday) and 'Feier' (celebration/party). 'Geburtstag' itself is made up of 'Geburt' (birth) and 'Tag' (day). A 'Geburtstagsfeier' is therefore literally a celebration for a birthday.
Die Kinder freuen sich schon wochenlang auf die Geburtstagsfeier.
The children look forward to the birthday party for weeks.
When holding a birthday party, you often use the verbs 'organisieren' (to organize), 'planen' (to plan), or colloquially also 'geben' (to have/throw) or 'schmeißen' (to throw).
Meine Freunde schmeißen für mich eine große Geburtstagsfeier.
My friends are throwing a big birthday party for me.
Pay attention to the prepositions: you invite someone 'zu' einer Feier (to a party) and go 'zu' einer Feier (to a party). If you are already there, you are 'auf' der Feier (at the party).
Kommst du am Samstag zu meiner Geburtstagsfeier?
Are you coming to my birthday party on Saturday?
party
'die Party' and 'die Geburtstagsfeier' can both mean a celebration with guests, food, drinks, or music. However, 'die Party' is more general: the occasion can be a birthday, but it does not have to be. 'die Geburtstagsfeier' names the occasion exactly, namely someone's birthday. Learners may confuse the words because a birthday party can also be a party. If the birthday is important, 'Geburtstagsfeier' is more precise. If the focus is simply on celebrating, 'Party' sounds more natural.

Für ihre Geburtstagsfeier hat Anna einen Kuchen gebacken.
Anna baked a cake for her birthday party.
Am Samstag geht Tom auf eine Party mit Musik und vielen Leuten.
On Saturday, Tom is going to a party with music and lots of people.