The random function gives you a random number. For example, random(5) returns a 0, 1, 2, 3, or 4. random(63) gives you a random number between 0 and 62.
Here is a program I wrote
strokeWeight(4);
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
point (random(400),random(400));
Type it in and run it a couple of times. Notice how the output changes each time you run the program.
Watch this video to understand what is going on (FunProgramming #3):
Change the stroke to random and get colored points
stroke(random(255), random(255), random(255))