Have got means exactly the same as have in most cases. The got-forms are more common in an informal style.

He has got a new girlfriend. (More natural than ‘He has a new girlfriend.)
Has she got a car? OR Does she have a car? (More natural than ‘Has she a car?’)

Got-forms of have (and forms with do) are especially common in questions and negatives. In fact, in American English have is not normally used without got in questions and negatives.

Compare:

She hasn’t got a car. or She hasn’t a car. OR She doesn’t have a car. (British English)
She hasn’t got a car. OR She doesn’t have a car. (American English)
Have you got my keys? (More natural than ‘Have you my keys?’)

They do not have adequate facilities. OR They haven’t got adequate facilities. (More natural than ‘They have not adequate facilities’.)

Notes

Got forms of have are not normally used in short answers or question tags.

‘Have you got a new car?’ ‘No, I haven’t.’ (NOT No, I haven’t got.’)
She has got a new car, hasn’t she? (NOT …hasn’t she got?)

Got-forms of have are not very common in the past tense.

I had flu last night. (NOT I had got flu last night.)

Got is not generally used with the infinitive or -ing forms of have.

Got is not used with the do-forms of have.

Do they have a car? (NOT Do they have got a car?)

In British English have without got is possible in questions and negatives, although it is formal.

Have you a meeting today? OR Have you got a meeting today? OR Do you have a meeting today?