How do payment processing companies work? What is the rationale for existence of payment companies like BitPay? If I want to start accepting Bitcoin at my store I can simply set up my own Bitcoin wallet for free and then a simple script which counts Bitcoin price after checkout depending on current exchange rate. So what is the extra value these guys bring to the system?
Currently still, most companies want to receive in fiat currency. Most of these merchant payment companies function as a man-in-the-middle, so that you don't have to be concerned about anything Bitcoin-related.

They provide functionality with which your customers can purchase goods using Bitcoin and you will receive all payments in your fiat currency of choice (as long as it's supported by the merchant service).

Like with PayPal, when a users wants to pay with Bitcoin in your site, they will get forwarded to a page from, f.e., BitPay. The user will pay in Bitcoins to BitPay and be forwarded back to your site while you will be notified that the users did indeed pay. Meanwhile, BitPay adds the payment amount to your merchant account, in fiat currency, using the exchange rate of that moment.

Given the high volatility of the Bitcoin exchange rate, this is the best solution for most merchants for now. It's easy and safe.