A simple way to differentiate raster and vector images is to think of photos as raster images and type and logos as vectors.
Raster (or bitmap) images are fixed-resolution images, made of a grid of pixels. If enlarged they will be blurry and pixelated, with a “stair-stepped” edge.
Common raster file formats are jpg, gif, tiff, bmp and png.
Vector images can be enlarged to any size with no loss of resolution.
Vector images are created by a series of points that are joined using a mathematical formula that determines the vector between points.
A purely vector file format would be svg (scalable vector graphic). Adobe Illustrator files are typically vector, but Illustrator supports placed raster images, just as Adobe Photoshop files now support vector layers. Pdf and eps files also support both vector and raster images, so asking for an Illustrator, pdf or eps file does not guarantee that you’ll end up with vectors. If you need vectors, ask for a vector file. It may be delivered as an eps, pdf, svg or ai file.
You should have your logo in a vector format, so that it can be reproduced at any size. Ask your designer for a vector pdf with type converted to paths to guarantee excellent reproduction at any size.