A vector logo design is a scalable version of your logo that is usually created in Adobe Illustrator. Vector logo designs maintain clarity whether they are sized for something as small as a business card or as large as a billboard. Printers often request your vector graphics to ensure your logo looks nice and crisp on your print materials, no matter the size. To easily see if you have your vector logo files on hand, look for files that end with .AI or .EPS, which are usually vector files.
Unfortunately, most discount logo designers do not give you access to your vector files because they resell your same logo design over and over again to other customers. For that reason, they usually retain the rights to your logo vector files. However, a custom logo designer will almost always give you the vector files because they design your logo specifically for you.