This is the 50th most frequent Turkish word.
ama
"Ama" means "but" in English.
Here, 'ama' is used to contrast the pleasant weather with the decision not to go out.
Hava güzeldi ama biz dışarı çıkmadık.
The weather was nice, but we did not go out.
Here, 'ama' is used to introduce a contrast between the desire to read the book and the lack of time.
Bu kitabı okumak istiyorum ama hiç zamanım yok.
I want to read this book, but I have no time.
In this case, 'ama' contrasts the option of inviting and the assumption of his lack of willingness to come.