When the proposal is "we have a bunch of functions that match functions used in other languages, lets add a few more from the same category of functions that we missed", does there really need to be much explanation beyond "they're useful in the other languages that have them, they'd be useful for the same reasons in Swift"?
If requested, I can provide examples of usage. But if you're not already sold on the benefits of working with sequences in a functional manner, it's out of scope of the proposal to convince you of the merits of that style of programming. And if you are already sold on the benefits of doing so, then adding these functions shouldn't need much explanation.
Here's a few toy examples, if it helps:
// list of all powers of 2 below some limit
iterate(1, apply: { $0 * 2 }).takeWhile({ $0 < limit })
// first "word" of a string, skipping whitespace
let cs = NSCharacterSet.whitespaceCharacterSet()
String(str.unicodeScalars.skipWhile({ cs.longCharacterIsMember($0.value) })
.takeWhile({ !cs.longCharacterIsMember($0.value) }))
// running total of an array of numbers
numbers.scan(0, combine: +).dropFirst()
// infinite fibonacci sequence
iterate((0,1), apply: { ($1, $0+$1) }).lazy.map({$1})