Kind of and sort of are both used to indicate that something is similar to a certain extent, but not exactly the same. /not exactly, but a little. They soften other words and phrases so that they do not appear too direct or exact. They are often used to express uncertainty or approximation.
These phrases are often used in informal speech to soften the impact of a statement or to convey a sense of hesitancy or reservation. They add a sense of being imprecise, vague. They should therefore be avoided in formal writing.
Kind of is more common in American English. Sort of is more common in British English (source):
I kind of like that movie (=you somewhat like the movie, but not completely).
She's sort of busy right now (=she is somewhat busy, but not overwhelmingly so).
He’s kind of jealous that they have become such good friends.
I’m sorry but she’s just kind of lost interest in buying the car.
They said it was a chalet but it was more like a sort of wooden hut.
She’s spent the whole year sort of travelling around the world.