Most of the time, it feels to me just like a logical conclusion. Like "hmm, yes, this person has traits I generally find attractive. I am thus attracted to them."
There's of course a physical attribute to it too, where I feel strongly drawn to the person, but it feels more like the result of the previous logical conclusion rather than the source of the attraction itself.

The one and only exception to this that I've experienced thus far was my attraction to my wife. It was an instant click. My first thought after meeting her was that I needed to get closer with her. It's worth noting I didn't actually know what she looked like yet (we met online) and barely knew anything about her personality besides she was funny and apparently had similar hobbies to me (though I didn't know which hobbies, I'd just been told that.)
I didn't connect it as attraction at first though, because I'd never experienced attraction like that before. I just wanted to be really good friends with her. I was really happy whenever she showed up. I enjoyed every conversation I had with her way more than it felt like I should.
Then slowly those feelings grew, never changing, only getting stronger. At a certain point, when I started to realize every second I was away from her, I was wishing she was there, and every time I was sad or upset about something, she was the one I wanted to go to for comfort, it finally clicked that I was attracted to her, at least in some way.
It wasn't until we were already dating that it finally fully clicked that I'd been in love with her the whole time.
Physically I'd say my attraction to her felt... I guess like heart burn? That's the closest physical sensation I can think of. Like that, but not painful. Like a fullness in my chest every time I thought about her.

Also as far as chemistry and attraction goes, definitely different things. There are people I've been attracted to that I meshed horrifically with. Just because I like certain traits in theory doesn't mean I could actually stand those traits in practice.