When getting a logo designed, make sure the Graphic Designer is working in the Adobe Creative Suite program ILLUSTRATOR, no exceptions!
Galan Graphic offers the correct format for a logo file/design. You can create other formats (JPG, PNG, etc) from the EPS/vector file.
I found this definition in Wikipedia:
Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygon(s), which are all based on mathematical expressions, to represent images in computer graphics. “Vector”, in this context, implies more than a straight line.
Vector graphics are based on vectors (also called paths, or strokes) which lead through locations called control points. Each of these points has a definite position on the x and y axes of the work plan. Each point, as well, is a variety of database, including the location of the point in the work space and the direction of the vector (which is what defines the direction of the track). Each track can be assigned a color, a shape, a thickness and also a fill. This does not affect the size of the files in a substantial way because all information resides in the structure; it describes how to draw the vector.
Example showing effect of vector graphics versus raster graphics. The original vector-based illustration is at the left. The upper-right image illustrates magnification of 7x as a vector graphic. The lower-right illustrates the same magnification as a raster (bitmap) graphic. Raster images are based on pixels and so when scaled there is a loss of clarity, while vector-based graphics can be scaled by any amount without degrading quality. (image from Wikipedia)