I often hear that the word "often" is pronounced as /ɔftən/ (mostly by Americans). My dictionary gives me the same transcription along with /ɔfən/. So what's the difference?
There is no difference. You can choose the pronunciation you prefer. I don't know if the first option is used mostly by Americans. I use the second one.
I use the second one, too. The first one I might use if I am being careful about the way I speak (i.e., in using emphasis).
Note that, the /t/ in /ɔftən/ is often not produced because to make the sound [t] you have to stop the air in your larynx/windpipe from flowing. The sound before it, [f], and the sound after it, [ə], don't stop the airflow. With those sounds, the air flows freely, continuously through your windpipe.
[ɔ'fən] has continuous airflow, whereas [ɔf'tən] does not: it requires more energy to produce, which is why the /t/ is often not produced.
Both are perfectly interchangeable, both in the US and UK, Australia etc.
We knew, when I was at school, that those who sounded a 't' in 'often were NQTD, 'not quite top drawer'.
I was taught that it was 'wrong' to pronounce the /t/ and it was discouraged at my school, though some used it.
I've come across people who used either pronunciation.