How to choose a laptop: memory and hard drive

The word memory usually refers to computer's "short-term memory" or RAM (Random access memory). Hard drive or hard disk is its "long term memory."
When you turn on the computer things that you and obviously your processor is working with get stored in the RAM. If you open a program (Word, browse the web, listen to music) it gets stored in the RAM, that means your computer is working with it (just like our short term memory). Once you shut down your computer, all of that gets erased (unless you saved it).

Saved it??????????????
But you just said it gets eeeerased.

When you save things, you save them onto the hard drive. Contents of the hard drive don't get erased when you shut down your computer (but you should still BACKUP YOUR DATA just in case). So that important essay, save it onto a USB stick too.

RAM: If you just use your computer for everyday tasks like web, music, movies or essays, then you need at LEAST 2GB of RAM if you have Vista or Windows 7 (4GB of RAM is better).

Hard disk (HDD): The more gigabytes the better.

There are two types of hard drives: ones that spin and ones that don't. The standard type of hard drive is a one that has platters that spin. In this type of HDD you want it to spin fast 7200RPM (Revolutions per minute) is better than 5400RPM. Et ceteris paribus more RPMs means faster file transfer.

The new type of hard drive is called "Solid state hard drive" (SSD). These ones don't have any spinning parts. They need less energy (longer battery life), they are generally faster and sweeter. The downside: they are expensive. Again if you are on a budget, skip them.