RAM (Random Access Memory) is a generic name for any sort of read/write memory that can be, well, randomly accessed. All computer memory functions as arrays of stored bits, "0" and "1", kept as some kind of electrical state. Some sorts support random access, others (such as the flash memory used in MP3 players and digital cameras) has a serial nature to it.
A CPU normally runs through a short sequence of memory locations for instructions, then jumps to another routine, jumps around for data, etc. So CPUs depend on dynamic RAM for their primary memory, since there's little or no penalty for jumping all around in such memory.
There are many different kinds of RAM. DRAM is one such sort, Dynamic RAM. This refers to a sort of memory that stores data very efficiently, circuit-wise. A single transistor (an electronic switch) and a capacitor (charge storage device) store each "1" or "0". An alternate sort is called Static RAM, which usually has six transistors used to store each bit.
The advantage of the DRAM is that each bit can be very small, physically. The disadvantage is that the stored charge doesn't last really long, so it has to be "refreshed" perodically. All modern DRAM types have on-board electronics that makes the refresh process pretty simple and efficient, but it is one additional bit of complexity.
There are various sorts of DRAM around: plain (asynchronous) DRAM, SDRAM (synchronous, meaning all interactions are synchronized by a clock signal), DDR (double-data rate... data goes to/from the memory at twice the rate of the clock), etc. These differences are significant to hardware designers, but not usually a big worry for end-users... other than ensuring you buy the right kind of DRAM, if you plan to upgrade you system.
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