A colloquial form of 'amari' used with negative sentences to mean ‘not very’ or ‘not much’.
その映画はあんま面白くなかった。
That movie wasn't very interesting.
あの店の料理はあんまおすすめしないよ。
I don't really recommend the food at that restaurant.
あんま無理しないでね。体を大事にして。
Don't push yourself too much. Take care of your health.