"have had" is the present perfect of 'have'. It's formed from the appropriate (conjugated) form of 'have' as the auxiliary + the past participle of 'have', which is 'had'.
It's used in the same way as any other verb in the present perfect.
"I have had a cat for three years." (I've owned a cat for 3 years)
"She has had a headache for the last week."
eat: I have eaten, he has eaten ...
have: I have had, he has had ...