We’ve spoken about “thing” recently, so here, I’d like to draw your attention to the weak vowel /ə/ for “a”, and for the first syllable of “about”. This sound is very common for unstressed vowels, and is made with the mouth just slightly open, and completely relaxed. It requires practice. It’s also good practice to listen for this sound when listening to a song or watching TV in English.
This phrase usually means “I really like..” or “I’m slightly obsessed with..”, for example, “I’ve got a thing about English pronunciation.”