A grave event or situation is very serious, important, and worrying.

A grave person is quiet and serious in their appearance or behaviour.

In some languages, such as French, a grave accent is a symbol that is placed over a vowel in a word to show how the vowel is pronounced. For example, the word 'mère' has a grave accent over the first 'e'.

A grave is a place where a dead person is buried.

If you say that someone who is dead would turn or turn over in their grave at something that is happening now, you mean that they would be very shocked or upset by it, if they were alive.