RAM, or random access memory is the temporary memory that the computer uses to perform its functions while being used; that is, the when the computer is actively running, it is constantly storing and erasing bits of information. When you shut off your computer, that information is gone. It is like using a whiteboard with erasable ink: you can use it over and over and over, but once you erase something, it is gone forever; unless you recreate it from scratch.
ROM, or read only memory. In its pure form, ROM is the data that is permanently written to a chip, that there is no way of overwriting. An example of ROM is the program that you computer uses to reboot. It is essential to the core functioning of the computer. You might be familiar with Electrically Erasable Programmable Read Only Memory in the form of a flash drive.