why cloud platforms are getting more popular now a days as though they are costly?

Currently i am trying to learn various Services of Amazon web services and Microsoft windows azure like Amazon sns,Amazon Storage,amazon Search.

I am having some question in my mind that why now a days cloud platforms are getting so popular than old traditional approach like previously we were storing our files(img,txt,.doc etc) in our web application project only but now adays some web application are storing their files on amazon storage or on azure storage.

What is the benefits of storing files and folders over cloud platform ??

Next why amazon search or azure search is preferred as when they were not available searching was done and amazon and azure search are not freely availabale??

Now if we talk about push notification then why to use amazon or azure push notification if we can easily send notification through codes that are available on internet??

I general i just want to know that why now a days web application are using more cloud platforms(Azure or amazon) even though they are costly??

Can anybody explain me this with some details??