"SSL" stands for "Secure Socket Layer" - this is the technology for securing connections when you transmit confidential information to a website. As when a purchase is made online. Any time the website address you are looking at starts with "https" rather than "http", you are looking at a secure, encrypted connection. The "s" stands for secure.
Typically your browser indicates this by a lock symbol in the lower right corner of the screen.
Part of the process is the website having an "SSL certificate" - which is an electronic certification that the company is who it says it is.
There are usually two ways you can get an SSL cert for your website. Most website hosting services will provide a "shared" certificate as part of your hosting fee (or may charge a small yearly fee for this).
The difference is on secured screens (https) during the checkout process, with a shared cert, the URL would not be your own domain, but is based on the hosting company's domain, for example, frogsales.hostingcompany.com. instead of www.frogsales.com.
This has nothing to do with the look of the site, it is just the page address.
Most hosting companies will sell you your own cert, but there are other certificate authorities you can buy a cert from. The most well known (and expensive) is Verisign.
SSL certs vary in features and vary widely in cost. If you do get your own cert, part of the process is varying degrees of proof of who you are. More expensive certs also usually involve more definite proof of your company's legal existence and physical location.
In most cases there is little value in purchasing a high end cert.