High speed internet commonly implies broadband internet service and is generally defined as internet access which is faster than dial up internet. Technical definition of broadband is a technology that allows companies to transmit multiple streams of data over one cable or channel.
Dial Up Internet service has been a mainstay of the Internet for well over a decade with several great companies leading the way from AOL (America Online) to CompuServe to Earthlink we have seen several giant internet service providers come (and some go) over the years.
Mobile Internet lets you acccess the Internet via your cell phone using smartphone technology. If you have a smartphone like a Blackberry, iPhone or Android, you have a built-in way to access the Internet. You can probably use a web browser, as well as email and maybe even some other applications.