Clefting is a way of bringing prominence to one part of a sentence by dividing it into two clauses. Almost any constituent of the sentence can be the target of the cleft.

In English the targeted constituent is introduced with a fairly meaningless wording such as 'It is...', and the remainder is a relative clause consisting of the rest of the sentence. For example, with

Leopold Bloom ordered a glass of Burgundy in Dan Byrne's pub.
any of the subject, object, or location phrases can be brought forward across the cleft:
It was Leopold Bloom who ordered a glass of Burgundy in Dan Byrne's pub.
It was a glass of Burgundy that Leopold Bloom ordered in Dan Byrne's pub.
It was in Dan Byrne's pub that Leopold Bloom ordered a glass of Burgundy.
You can also sometimes extract from within constituents. Both the noun phrase 'a glass of Burgundy' and the prepositional phrase 'in Dan Byrne's pub' contain smaller phrases. Only one of the potential extractions from each is in fact grammatical. (It would get too far off the track to explain why, as the teacher says when they don't know.)
It was Burgundy that Leopold Bloom ordered a glass of in Dan Byrne's pub.
* It was a glass that Leopold Bloom ordered of Burgundy in Dan Byrne's pub.
It was Dan Byrne's pub that Leopold Bloom ordered a glass of Burgundy in.
* It was pub that Leopold Bloom ordered a glass of Burgundy in Dan Byrne's.
* It was Dan Byrne's that Leopold Bloom ordered a glass of Burgundy in pub.
This is the construction that is normally simply called a cleft sentence, or sometimes an it-cleft. Similar in effect is a pseudo-cleft sentence or sometimes wh-cleft, where a relativized question (in English beginning with wh) is wrapped around the rest of the sentence, then equated to the targeted constituent:
What Leopold Bloom ordered in Dan Byrne's pub was a glass of Burgundy.
What Leopold Bloom ordered a glass of in Dan Byrne's pub was Burgundy.
Where Leopold Bloom ordered a glass of Burgundy was in Dan Byrne's pub.
For reasons that temporarily mystify me, though I should be able to justify them, you don't seem to be able to put the subject into a pseudo-cleft:
* Who ordered a glass of Burgundy in Dan Byrne's pub was Leopold Bloom.
Both clefts and pseudo-clefts have alternatives with 'one', and curiously, this makes the previous example grammatical:
Leopold Bloom was the one who ordered a glass of Burgundy in Dan Byrne's pub.
The one who ordered a glass of Burgundy in Dan Byrne's pub was Leopold Bloom.
In clefts the targeted element comes first, in pseudo-clefts last. But they are not just mirror images of each other, since you can have an inverted pseudo-cleft, swapping the order of the halves around the cleft:
A glass of Burgundy was what Leopold Bloom ordered in Dan Byrne's pub.
There are other constructions of the clefting type, such as the all-cleft:
All Leopold Bloom ordered in Dan Byrne's pub was a glass of Burgundy.
However, this adds a specific element of meaning, 'all' in the idiomatic sense of 'only'. The main kinds of cleft sentence don't change the meaning at all, but introduce prominence of some kind to one of the elements. In normal intonation, it is what I've been calling the targeted element that gets the emphasis: it is one element isolated from the rest of the sentence:
It was Leopold Bloom who ordered a glass of Burgundy in Dan Byrne's pub.
What Leopold Bloom ordered a glass of in Dan Byrne's pub was Burgundy.
But this takes us into the choppy waters of focus, topic, and emphasis. It's not really emphasis, it's not that you raise your voice on the isolated part, but that part is what's new, compared to the rest of the sentence, which is what's old or given. The new part is what counts as the answer to a question:
Who ordered a glass of Burgundy?
It was Leopold Bloom who ordered a glass of Burgundy.
What did Leopold Bloom order?
It was Burgundy that Leopold Bloom ordered.
What Leopold Bloom ordered was a glass of Burgundy.