Images can be in many formats. Some are perfect for web use while not suitable for printing. Some images can be printed in a large format (billboard size) while others are too poor a quality to be printed as anything larger than a passport size photograph. The reason behind this is largely based on the type of file that the image is stored as.
Essentially the vast majority of images that people work with are all made up of pixels, a series of tiny squares of varying color and hue that make up the whole image. An image that is made up of 72 pixels per inch would typically be an image that you see online – if you tried to print that image any larger it would look pixellated or grainy. Images that are of a higher resolution (example 600 pixels per inch) would be of a much better quality when printed. These files are recognizable as Jpegs or bitmaps.
It is possible to convert or “vector” a bitmap image to a vector image. This would essentially convert and trace those pixels into shapes such as circles which then allows for scaling to larger images without losing quality or distorting the image. A vector image is not limited by the number of pixels per inch. Vectorising an image can take a photo and turn it into an illustration through tracing (which is either done by hand or automatically through the use of software with this feature built in).
A benefit of vectorising is a more of a practicality – if you have lost your original logo design you could scan a copy (from a letterhead or business card) – this would most likely scan as a bitmap which would look pixels and of poor quality, converting it to vector would allow manual (or automatic) tracing, color matching and image quality improvement. Once this is done you can always convert back to a bitmap version for use on your website or re-print business cards.
The advantage of having a vector image is the scope of editing, enhancing and media-friendly mediums. Most graphic designers will start images in vector and then convert to bitmaps, jpegs depending on the purpose of the graphics. A website would not have a vector image on its page as it is not necessary to have that level of quality on a screen however a billboard print would most likely use a vector image.
The best file types to undergo a conversion to vector are jpeg, png, gif, bmp, tiff and psd and there are a number of software options available to manage this process. The most popular are Adobe Illustrator and Corel Draw.
There are also a host of service providers that will manage that process for you if you do not have suitable software available or lack the know-how.
Ultimately, the decision to work in vector or bitmap imaging will depend entirely on the purpose of the image.