A cleft sentence is a special structure used for emphasizing particular words or phrases. In a cleft sentence we put everything into a kind of relative clause except the words we want to emphasize. These structures are useful in writing because we cannot use intonation for emphasis in written language. They are also common in speech.

Study the following examples.

Alice works in a restaurant.
Alice is the person who works in a restaurant. (Emphasis on Alice)
The person who works in a restaurant is Alice. (Emphasis on the person)
A restaurant is (the place) where Alice works. (Emphasis on restaurant)

John gave me a watch.
John is the person who gave me a watch.
The person who gave me a watch is John.
A watch is what John gave me.

John went to the market on Sunday to buy some meat.
Sunday was the day when/that John went to the market to buy some meat.
The day when John went to the market to buy some meat was Sunday.
The reason why John went to the market on Sunday was to buy some meat.
To buy some meat was the reason why John went to the market on Tuesday.

Notes
The place, the reason etc can be dropped in an informal style.

Why I am here is to talk about my plans. (Informal)
The reason why I am here is to talk about my plans. (More formal)

To emphasize a word we use a structure with what…do.

She cried.
What she did was to cry.
she writes short stories.
What she does is to write short stories.

To emphasize a whole sentence we usually use a cleft structure with what and the verb happen.

The cat died.
What happened was that the cat died.