In
phonetics, a roll is a sound made by repeatedly and quickly moving a free-standing part in the mouth. There are three objects that can roll in this way: the tip of the
tongue, the
uvula, and the lips. The resulting sounds are called a
lingual roll, a
uvular roll, and a
bilabial roll.
The lingual roll is the more familiar "rolled R" used in Italian, and in an exaggerated Scottish accent. Most English speakers notoriously have a hard time rolling their R's. Worldwide it's pretty common, and it's actually English that has the strange R sound.
What happens is that the tip of the tongue very quickly flicks up and taps the alveolar ridge behind the upper teeth. If it does this just once it's called a flap or a tap. (These two terms are distinct, but I'm not sure you could justify the difference in pure physical terms.) But if there are two or more taps/flaps in quick succession, it's called a roll. When an Italian or Finnish speaker produces a rolled [r] by itself they might make three to five taps. In normal connected speech there could be less: only two or three. There is no definite number. However, both Italian and Finnish have double consonants. Not only do they have a sound [r], they have a longer/doubled form of it, [rr]. This is sometimes called a trill, but again I don't think there is a definite physical definition of this. What you have is a single roll with two or more taps, and a double roll with more taps than the single one.
Much rarer is the uvular roll. In fact I find it very hard to perform: I'm not sure that I can do it at all. If you know the singers Edith Piaf or Jacques Brel, their striking rolled throaty R sound is the true uvular R. Most French speakers don't use this sound. Historically, it might have been that French /r/ changed from a lingual roll to a uvular roll. But this sound is difficult and unstable.
Modern French, and other languages that have this or similar R-sounds made in the back of the throat, such as German, Dutch, and Norwegian, have a uvular sound, but it's not a roll: it's not created by actually flapping the uvula freely in the air stream. Rather, it's a fricative. It's created by bringing the back of the tongue very close to the uvula, so that the constriction is tight and causes friction. Acoustically, this is very similar to the uvular roll sound.
Although Scots are stereotypically depicted as rolling their R's, in reality most Scots accents use a single flap/tap for their R. I did once hear a gloriously rolled R in a drunken Glaswegian accent, but it's very rare these days.
Uniquely in the world, the Czech language has a lingual roll that is at the same time a fricative. This is basically indescribable: the composer's name Dvořák contains it, and is usually pronounced with the "zh" sound of "azure, measure", because the Czech sound is roughly that simultaneously with a rolled R. Czech has this sound Ř as well as an ordinary rolled R.
Cletus the Fetus reminded me that the bilabial roll is also physically possible. This is the "brrr" sound you make with your lips when you're cold. For most of us this is paralinguistic (used for communication but not for language as such); but in recent years linguists were surprised to find it actually occurred as a normal speech sound in a few languages.