Computers have two types of storage system: primary storage and secondary storage. Primary storage or memory is directly connected to the motherboard and is the place where programs and data are kept while being used. Secondary storage is the place where software and data are kept when not in use. Some individuals (and references) use the term memory to refer to both memory and storage but we will use different terms on this Web site.
On modern computers memory is usually composed of semi-conductors known as RAM (random access memory). There are two technologies for RAM chips: dynamic RAM and static RAM. Dynamic RAM is much cheaper and has larger capacities. Static RAM operates much faster. (See "How RAM Works"). RAM is volatile, meaning that when power is lost, even for an instant, the contents are erased. Consequently, RAM is not suitable for long-term storage of software and data. The contents of RAM can be manipulated while the computer is running. The computer is capable of determining what an individual memory cell contains (a process referred to as "reading"). The contents of a cell can also be changed (a process referred to as "writing"). When something is written to a memory cell its former contents are lost. John von Neumann, a mathematician who was part of the team that created the first electronic computer, ENIAC, came up with the concept of putting a program into a computer's memory in order to run it. The ENIAC was designed in such a way that to run a different program the computer would have to be turned off and rewired. With von Neumann architecture the program(s) being run are kept in the computer memory as well as the data that is currently being processed.
ROM (read only memory) is another variety of memory. It is similar to RAM except that it has its contents permanently embedded and thus will not be erased when power is turned off. The contents of ROM cannot be changed. ROM is thus typically used to store software that needs to be available when the computer is turned on (such as the instructions for booting the computer) or software that will "never" change such as the BIOS.
Wikipedia article - Computer Data Storage
Wikipedia article - Random access memory
howSTUFFworks - How Computer Memory Works
howSTUFFworks - How RAM Works"
Kingston Ultimate Memory Guide