grandmother
In French, 'grand-mère' is used to refer to a person's grandmother. It is commonly used in both formal and informal contexts. It is a compound word, combining 'grand' meaning 'big or great', and 'mère' meaning 'mother'. It is pronounced as grah(n)-mair.
My grandmother makes the best strawberry jam.
In this French phrase, the speaker is saying that the strawberry jam made by their grandmother is the best. This is simply using 'Ma grand-mère' (my grandmother) to demonstrate possession, and then the verb 'fait' (makes) to signify the action of making the jam.
His grandmother lives in France.
Here, 'Sa grand-mère' signifies the speaker mentioning someone else's grandmother. 'Vit' (lives) is the verb that shows action and 'en France' (in France) gives us the location of the action.
Luc's grandmother is very nice.
This sentence shows a possessive phrase in French in another form where it's expressed as 'La grand-mère de Luc' (Luc's grandmother). This is often used for family and personal relationships.