Increasing RAM doesn't necessarily increase speed. Adding RAM helps you run more programs at the same time with less disk-reads. Disk-reads are what slows you down when you're out of free RAM space.
This is just an example, nothing really technical.
Let's pretend you have 100mb of RAM. 50 of it is being used by your browser. If you copy an image that is also 60mb it will have to store 10mb of it on the disk. So it will write it to the hard drive. Then if you paste, it has to read that 10mb on the disk, so it has to read. That's twice that the hard drive has had to be accessed.
Now let's say you increased it to 150mb RAM. 50 being used by the browser and 60 being used by the image you copied. It can store the image in its entirety in RAM, thus there is no need to access the hard drive and everything works quicker.
It's as simplified as it gets. More RAM allows more things to be loaded at once.