Specialized hosting takes into account the ramifications of different software solutions like Magento. Magento is a highly-tuned eCommerce solution with a lot of value to offer a determined online retailer. Maintaining it requires a significant hardware outlay.
It's possible to find server that are equal to a full Magento install. It has minimum system requirements just like any program. Many server-side software solutions do. It's perfectly possible to shop for hosting carrying these requirements in mind. It's much easier to find a dedicated hosting solution that acknowledges the needs of a software suite and caters to them.
This is particularly relevant from a perspective of customer service. A business that predicates it product marketing on compatibility with a particular software solution will be equal to much better support with that software solution. If you have any issues pertaining to Magento while using a Magento-specialized hosting plan, help will come easier.
Specialized hosting is a relatively new concept. It was once a factor only in the most broad-strokes purposes. It is now a much more viable business solution that can take a lot of time and effort off of your plate.