Hello @emilmoe,
Choosing between vector and raster graphics is a matter of what you are working on. I've simplified my opinion below and I hope this helps.
If you're working on wireframes and documents with shapes, lines, and colors then vector trumps raster. However, if you're working on documents dominated by photography or illustrations, then working with raster graphics is a better approach.
Vectors graphics are created with mathematical curves and paths while raster graphics (or bitmaps) are composed of pixels. Below is a diagram to show the difference between the two:

The benefits of vectors include:
One of the only disadvantage of vector graphics is compatibility. Not all applications support vector formats such as .SVG and .EPS. However, most applications which do support vectors, allow you to export them as rasters.
Vectors graphics are easily a better option. Try and use them in as many places where it's appropriate, and you'll slowly learn of the many advantages along the way.
Shaan Shivanandan
Design @ Capillary | Ex-Accenture | Ex-Digit Insurance | Srishti Institute Alumnus