I live in Slovakia and in certain parts this is a very common thing - if you're about to have a birthday/wedding/any other gathering, you book a restaurant or some bigger place, you agree on what meal they should prepare for you and they prepare tables. The waitresses are there for you as usual.

But when it comes to alcohol and drinks in general, the restaurant doesn't serve it, you bring your own and also serve it.

I always found it weird that we bring our own alcohol to a restaurant even though the restaurant offers alcohol aswell.

Is this common in your country also? Do you bring other things for a party/gathering in a restaurant?

Reviving an old thread, but in Ireland that is still a thing. Not so much in Dublin anymore, (it was until relatively recently) but definitely in the countryside or the smaller cities/bigger towns it is still a done thing.
When you bring your own, some places charge 'corkage' for it, which is essentially a charge for bringing your own alcohol with you, and charging you to open it.
Not all places charge corkage, and some do out of necessity, while many do out of greed.

Restaurant customer doing ‘dry December’ quoted €40 corkage for alcohol-free wine

Corkage was debated in the Dáil Éireann (the houses of parliament) earlier this year.