RAM is an abbreviation for Random Access Memory. This is a type of computer memory, that, unlike other storage devices such as harddrives or DVDs, allows the info to be accessed directly without reading the previous content stored in it. Anytime an app is started, it is stored in the RAM, because it can be accessed much quicker than if it was read from another media device. With regard to the website hosting service itself, additional RAM means that more web applications can work all at once on a given web server, especially if they are resource-demanding and are accessed by a significant number of people simultaneously. In contrast to a shared web hosting package in which the resources of a given account may be flexible and quite often depend on what other end users consume too, a VPS has a guaranteed amount of RAM which can be used all the time. That memory is assigned to one server only and won't be used by other clients even if it's not being used.
