In most cases (like the example), it simply allows you to call "effectful" code (often monadic, IO etc) to populate arguments of a function.
My favorite example is "I want to grab three web pages concurrently and return them in a single triple." To the haters who think this is just golf, just TRY to write this as beautifully in any other language.
(page1, page2, page3)
<- runConcurrently $ (,,)
<$> Concurrently (getURL "url1")
<*> Concurrently (getURL "url2")
<*> Concurrently (getURL "url3")
(taken from the excellent haddocks for Control.Current.Async https://hackage.haskell.org/package/async-2.0.1.4/docs/Contr...)