Despite what many hosts want you to think, having an online store doesn't have much to do with the actual server - this requires three components which any industry standard webserver can provide.
Some hosts sell you a "bundled" package of all these components, and label it as a store. Such providers include Yahoo stores, and Shopify.com. Hosting an online store is nothing magical - you just need a few basic components:
a. A store software suite - popular ones include ZenCart, CubeCart, and OsCommerce - this is what actually comprises your site and allows you to add, remove, and modify products, accept payments, have a "shopping cart" system, and handle your customer's user accounts. This serves as the link between your customers placing orders and you receiving them. This connects to your merchant account(b) through your SSL(c).
b. Your merchant account is what allows you to accept payments. The merchant account is set up between you and a merchant provider, and does not have anything to do with us - your store software connects through our server, to the merchant provider's server and sends it the credit card details your customer just typed into the store software's customer interface. The merchant provider then charges the customer's card, and moves the funds into your account with them. How you get paid by the merchant provider varies from provider to provider, but normally they will either deposit into your account directly, send you a check, or send you a PayPal payment. The credit card information, when in transit between your client's computer and your server must be encrypted for safety reasons. This is why you need an SSL certificate(c).
c. The SSL certificate can be thought of as a lockbox for your data - while it doesn't make it any harder for anyone to get ahold of the data, it encrypts it to the point that nobody can understand it. In addition to encrypting data, the SSL shows visitors that your business is legitimate, and will not attempt to defraud them in any way.
The SSL certificate can come from any SSL provider such as Comodo (HDWEBPROVIDER™'s provider), Verisign, GeoTrust, GoDaddy, etc. We also sell SSL certificates starting at $50 per year. If you buy one from us, we'll also install it for free, a $10 value. We also offer more advanced SSL certificates, such as the InstantSSL and EVSSL certs, though those are more expensive, and usually unnecessary.
The great thing about going with a host like us, instead of a "bundled" host like Yahoo stores, is that if one component simply isn't working to your satisfaction, you can replace it and only it. For instance, if your merchant provider is hiking your rates, you can keep your store, keep your host, keep your SSL, and replace your merchant provider. The same applies if you decide you prefer another store suite, or want a higher validation level of SSL.