The phrase comes from the gesture of taking off one's hat as a sign of respect. After that incredible performance, I take my hat off to the entire cast.
Pro Tip 2/3
Sincere Praise
Use it to sincerely commend someone's exceptional actions or achievements. I take my hat off to the volunteers who organized the charity event.
Pro Tip 3/3
Not Literal
It's a metaphor; people don't actually remove their hats when saying it. When I say I take my hat off to you, I mean I really admire what you've done.