The phrase "bite your tongue" means to stop yourself from saying something that you would really like to say but shouldn't.
For example I wanted to tell her what exactly I thought of her but I had to bite my tongue instead.
You should bite your tongue when you should not say a particular thing, even though you want to, because it would be the wrong thing to say at the time, or because you are waiting for a better time to speak.
I wanted to tell him how much I would miss him, but I bit my tongue.
Not to literally bite your tongue as that would hurt but you should not say something that you really want too as it may make things worse.