"They really seem to click."
Riding a strange horse is a difficult (and on occasion dangerous) proposition - in fact, many trainers have a kid with good stickability and the ability to bounce get up on the horse first. Just in case.
Even if nothing goes wrong, it can often feel as if you're flailing around looking for the horses "buttons." Ironically, it can be even harder with a horse that's at a higher level of training.
But sometimes, you can get on a completely strange horse and almost immediately everything flows together and works. "Clicking" is one of the terms we use for that. It's also used in other situations where a horse seems to go much better for one person than another.
So, what causes it?
1. With a strange horse, the "click" often happens if the new rider is similar in size, build, and riding style to the old one. The horse adapts more quickly (and relaxes more quickly - a lot of horses are very tense when a strange rider gets on them). It can look "mystical" but it just means that the rider's natural way of riding is closer to the way the horse was trained.
2. Sometimes horses really do like one person better than another. This can also relate to size and build - just as a rider is more physically comfortable on some horses, a horse can be more physically comfortable with some riders. Or they prefer how that person rides. Or...sometimes they can just take a liking to you (or a dislike, which can result in a disaster - I've known horses that are actively picky about who they "let" ride them).
To an outsider or a novice, though, it can look almost magical. "How come that horse won't do that for ME?"