застольная песня is a song (often its author can't be traced back) typically sung when people eat and drink at a holiday party, gathering. They are generally simple and traditional (it is often claimed that the author of such a song is PEOPLE - народ, and it can be called народная песня which is a more generic term), but a melody can be beautiful. The themes are often some events in Russian history, Russian nature, they may be sad or cheerful.

The classic example is Ой, мороз-мороз. Ой, мороз мороз - Oi, moroz moroz - YouTube

Some famous songs in this genre can be performed by эстрадные артисты (исполнители), хоровые ансамбли (folk bands) on the stage, so it's generally in the category of народная музыка.

As for Traviata (opera) it is probably a feast song (Western type), the same term has been used, but the meaning is different from traditional Russian застольная.