Those payment processors are basically there to make selling bitcoin (or buying), into your currency, easier for small/large businesses.
It allows businesses the ability to convert their btc faster than waiting for someone to come to their store and say,
"I see you sell rare books, do you also happen to have some btc for sale?". Most businesses still need to pay bills or employees in regulated currencies.
Bitpay for example, is about converting your "pay check" into bitcoin, I think with direct deposit into bitpay banks accts.
This is a solid explanation. Right now the way I see it is that these services act as a crutch - they help to prop up Bitcoin but they also prevent it from moving forward. The way Bitcoin works right now is it is seen more as a commodity (and an unstable one at that) rather than a currency. So merchants still want the business that comes with accepting it as a payment method without the risk of fluctuating value - and so they use Bitpay etc. as a means of getting fiat - while "accepting" Bitcoin. In reality though - it's just an onsell - Bitcoin isn't acting as a currency where it is accepted then kept and spent.