Why do I need vector files?
Things that are created using software that is vector based use mathematical formulas on a grid system... perfect for things like logos. Logos always need to represent perfectly no matter where they are placed and vectors allow a crisp edge at all times.
What about photoshop files?
Photoshop and other photo editing software uses a platform made up of tiny squares of colour information: pixels. These are raster files and are useful for photographic things, but not for anything that needs a clean edge - like words or logos.
If I zoom in on my vector files, they never lose their shape. There is always a crisp edge. As big as the moon or as small as a stamp, no quality is ever lost.
If I do the same on my raster files, I get to see the individual pixels that are made up of black or grey or white to make a curve.
Vector files for printing
Make sure you have your vector files saved. These are the ones needed to create the perfect end result if you're printing anything.