You know those things. Takes place in the past. Invites lavish production values like art direction and costumes—and usually cinematography while you're at it. It's kind of hard to define what defines "period" films per se—something that took place a decade ago could count, technically, but period pieces set in the very recent past are rare unless it's to poke fun at the era in question. Big budget period pieces are often dramas, frequently big epic ones, and take place at least thirty years ago.
Very often Oscar Bait. Sometimes it's based on literature that was contemporary when published, but feels like a purposesful attempt that recapture that era for new audiences. (Adaptations of Emily Brontë, Jane Austen, or Charles Dickens are especially common.) Useful if the period predates a Trope Breaker.
The BBC makes a lot of these, and PBS imports them wholesale. The BBC have sometimes even been accused of "falling back" on costume dramas when they've got into trouble for something or when the licence renewal is coming up and they need to show they can do some "proper" drama. That said, they're very good at making them: they usually garner a lot of praise, and the end result is packaged into box sets for sale during PBS pledge drives. As a side effect of their decades of Period Piece production, The BBC has accumulated a vast stockpile of costumes and expertise, which is occasionally raided by sister shows such as Doctor Who when they decide to do a historical episode.
There's no real need for examples. Just about any show set in the past counts. You'd know one if you saw one. Some Tropers restrict this trope to "any show set in the past that could have been set in the present", but that ignores the fact that it's impossible for most period pieces to be set in the present day because the plot and the characters' motivations would be nonsensical due to Values Dissonance. For example, setting Pride and Prejudice in the present day as is would make the crisis (Wickham's eloping with Lydia) seem inconsequential and the reaction silly, since the entire point of the crisis is that if Lydia doesn't marry Wickham and clear the family name, the rest of the sisters will end up as impoverished old maids because no gentleman will marry them. That's the way life was in 1812.