Vectors files, which include AI, WMF, SVG, EPS and PDF, are quite versatile provided you have image editing software to work with them. Unlike bitmap images (JPG, PNG, GIF), comprised of pixels, vectors are based on mathematical equations such as points, lines and curves. This makes them ideal for larger projects as they maintain the image's crispness and quality when enlarged significantly.
Another positive is that unless the vector you choose has been created with a coloured background that is part of the design, it can be saved as a new file with a transparent background (where the file format permits). JPGs, on the other hand will have a background 100 per cent of the time, while PNGs may have a transparent background, but there's no guarantee.
Vectors also make it easier to alter an image whether you want to change a colour, take something away or add to it. Should you find two images close to what you want, but neither is exactly what you're looking for on its own, choosing vectors will allow you to combine elements of both to create your perfect design.
Perfection, of course, can be elusive. Vectors can't be used in producing realistic photos as they don't possess a continuous flow of subtle colour tone and shade variations.
Also, as mentioned earlier, you will need image editing software to open a vector. Among the most popular are CorelDRAW and Adobe Illustrator. Photoshop can be used to increase the size of an image when you open it, but it will rasterize it meaning that the ability to work with the vector data is gone.
There are as well some free software programs available online. This site lists a number of options:
5 Best Free Graphics Software
To help you learn more about vectors here are some informative sites:
Tech-Faq Vector Information
Web Designer Differences Between Pixel and Vector Graphics