Apericena is a portmanteau word made up of aperitivo and cena, and this relatively new custom in fact is a combination of a drink (usually alcoholic) and a buffet dinner, with an affordable all inclusive price tag.
The aperitivo has been around a long time, and the word refers both to the drink before the meal and the custom itself, which involves having a drink with perhaps a very light snack before a major meal. The difference between aperitivo and apericena is that the latter does not precede the meal, but replaces the meal. And the meal is not the usual sit down affair with two or more courses, but a buffet. So that the apericena is a way to save both money and time and have some fun, too. In practice, there is often overlap in the usage of the two words.
It will be fairly obvious that this is similar to our happy hour. Music and (alas) karaoke are often featured. But, being in Italy, you can be sure that the drinks and food will be better. I'd definitely give it a try.