A vector file is a professional file of any graphic, which can be blown up to a huge size without losing any quality as it's not made out of pixels like a regular photo file.

Usually the file is saved as .ai or .eps and sometimes as .pdf. It does not mean the PDF is a vector file, but it could be.

The only way to find out is to open it in a program like Adobe Illustrator to see if it is or not.

You cannot view an .eps or .ai file unless you have a professional graphic design program.