You're talking about the poem, I guess.
It's a legal issue, really. You're allowed to make fun of people, covered from several angles by law.
But you're not allowed to simply insult someone. There is a difference.
What Böhmermann did was the latter.
It went down like this:
He said "I gonna show you the limits of what current laws allow as explanation why extra3 with their song did everything right. It will be not allowed by law. It will be removed by the station. It will be removed from the internet as far as the station is concerned. Remember, this is not allowed, it's called "Schmähkritik"."
He then started reading the poem which simply consisted of insults directly aimed at the person Erdogan, not connected to his status, his actions... purely personal insults.
And that is not allowed.
If he faces legal consequences for it, that is fine by me.
There is a fine line between satire and just insults. He crossed it. He might get fined for it.
He is a very smart guy. He knew perfectly well what he was doing.
It's national law. Has nothing to do with Turkey, refugees or anything political. If I post a video saying "Angela Merkel is a fucking b***h!", they'll come after me. If I post a video saying "Max Mustermann, my neighbour, is an asshole.", Max Mustermann can sue me and I will be fined.