The following will try to explain the difference between a Bitmap and an EPS file with showing an example using the star bucks logo:
I will explain the very basic understanding for each type. View the image below and notice on the left hand side the image is blurd. On the right side you can see the image is very sharp. This is because the image has been created in a line format and then filled as shapes.

Raster images or Bitmap are being defined by pixels, it can also be used for prints by creating your subject on a higher DPI (dot per inch) platform, but the higher the DPI the higher the file size will be, once you finished your raster work, it will never have the same quality when you re-size it to higher multiplicand. (this is a common format on the web and photographs)
Vectors are mathematically-defined geometric shapes-lines, objects and fills, they are being made by mathematically putting together nodes and points to create a shape which means resizing a vector image will multiply the factor according to how much you wanted them to be. (This is useful on printing such as a 20 foot billboards without losing quality and running out of storage for file size.)
So once it has been created as an eps file it's in a format which is very clear. See the image below.

So thats it, using the vectorised format I can do anything to the logo with Photoshop or Illustrator. You can see it's now in a line format so we can send it to our laser cutters and cnc routers. We have it in a format which we can now bring to life.
