You can create your logo in different formats, depending on your needs.
The main reason to having a logo in vector format is that you can adjust the size and edit the logos components using graphics software. Vector formats also allow you to enlarge your logo to any size without any loss of quality. Vector graphics are designed to give you the best quality image regardless of the size, your logo will never be pixelated.
Your logo will not only be constantly high quality, it will also weigh less and and be more detailed. This is one of the main reasons why vector formats are used for websites and printed stationary products. Professional web designers in the web and printing business usually ask for vector graphics when designing websites and print stationary products.
The bottom line is: You should be able to download your logo in different formats in order to be able to use them freely on all types of media.