Baracca sounds somewhat similar to "barrack." Barracks (a plural word often expressed in the singular) refer to a building or group of buildings that house large groups of people, often military personnel. It comes from the 17th-century French word "baraque," which in turn comes from the Catalan "barraca" (hut), of uncertain origin. The Italian word is baracca. It's a humble word about a humble place, but Italians use the word to mean a variety of things and not always humble ones.
It's hard to know what uses came before others, but let's first look at a very common Italian expression that might not make sense to a non-native.
We can imagine, perhaps, street performers who set up a little theater (baracca) with puppets or marionettes (burattini). Then the police come their way and they have to fold it up quickly and skedaddle. Or, perhaps the audience is booing. The puppeteers grab their things and hightail it. So in this case, la baracca is another word for teatro di burattini (marionette theater).
So when you up and leave with your stuff, you can say:
Chiudo baracca e burattini e me ne vado. I'm closing up shop and leaving.
Note that some people use the verb piantare, which aside from meaning "to plant," can also mean "to abandon."
Pia, la mia colf, mi ha piantato. Dice che non vuole vivere in campagna.
Pia, my nanny, ditched me. She says that she doesn't want to live in the country.Play Caption
Piantare baracca e burattini. Using the verb piantare really gives the idea of just up and leaving: abandoning ship.
If we look at some Italian dictionaries they mention that the expression chiudere/piantare baracca e burattini implies a brusque interruption of whatever the status quo is, for example, leaving a job all of a sudden, quitting school, or leaving one's family. On a broader, figurative level, it can mean completely changing the horizons of one's existence.
Baracca e burattini e si torna a casa, hai capito?
Theater and puppets [leave the whole shebang] and you go home, you get it?
Caption 54, Moscati, l'amore che guarisce EP1 - Part 6Play Caption
The nurse left off the first word of the expression, which would have been either chiudi or pianta. In English, we might even say, "You take your toys and go home..."
With this common and beloved expression out of the way, let's look at situations where the word baracca is used on its own.
In the following example, we're talking about a state-run health center:
Intanto questa baracca ha un responsabile e si dà il caso che sia io.
In any case this shack has a person in charge and it happens to be me.Play Caption
In this example, la baracca represents a business:
Poi Bianciardi muore, viene ammazzato, e Lei diventa proprietario di tutta la baracca, che dice?
Then Bianciardi dies, he gets killed, and you become owner of the whole shebang, what do you say?
Captions 16-17, Il Commissario Manara S1EP9 - Morte in paradiso - Part 10Play Caption
Here, it's a household:
Come farà Libero con i piccoli? Eh, hai fatto bene a pensarlo, perché non è facile qua, la baracca...
How will Libero manage with the little ones? Uh, you were right to think about that, because it's not easy here, the shack...
Captions 25-27, Un medico in famiglia Stagione 3 S3 EP1: Ciao famiglia - Part 8Play Caption
Here, it is another business:
Melody non ha la responsabilità di mandare avanti la baracca.
Melody isn't responsible for keeping the shack [things] going.
Caption 31, Sposami EP 4 - Part 6Play Caption
The expression mandare avanti la baracca is a very common expression with the word baracca, meaning "to keep the show going." Literally, "to send it along."
Keep your eyes and ears open for more expressions with baracca. Now you know what it means!