A vector line is a math representation of a line with either two end points or one starting point and a direction - all just numbers.

Raster is a bunch of dots in a grid which have colors assigned to them to make up the image.

Rasterizing is where you go from something into a raster set of pixels. So what happens is that the app runs down the math line and colors in the dots. Its a little more complex than taking the closest and making it black on a white background for example as most measure the distances from the exact math line to the square pixel position and shade it darker the closer you are so it looks smoother and better.

So apps like say inkscape can export the math vector data to a raster version where it will do all that processing for you and leave you with a rastered bitmap - a rectangular set of pixels stored in a container like a JPG or a PNG.

Going the other way involves looking at the rectangular set of pixels and trying to best fit a line onto the darker pixels. Thats a more inexact science and different programs will give different results - some better than others.