The DOM of a page is org'd as a tree. Dig it? No? Go read a book.
I can go on about how the DOM element is built like a tree, with "parent" and "children" elements, but like I said: Go read a book.
Here's an unordered list:
children(): gets all the child elements of the matched elements xcept text nodes
prev(), next(), parent(): walks the tree - like I said about reading a book
find(): search within a given element to find elements that match the expression
each(): loops over a set of matched elements and calls a function for each