Digital photographs contain a limited amount of information in the form of small squares called pixels. Whether the images come from a digital camera or are scanned from film, once they're in the digital world they can't be enlarged. There is no way to increase their resolution (meaning size), which is measured in pixels per square inch. The recent photograph above of my daughters and I in San Francisco's Chinatown, was taken with an older iPhone and you don't have to zoom in much to see the pixels in my wolf daughter's face. And while a larger version would be really nice (this one isn't big enough to fill the photo area), there is no way to add new pixels. Which means, among other things, that it's time for my husband to get a new iPhone.
It's true that CSI lab technicians and Angela on Bones will zoom in to a photo from an old security camera and sharpen up a small area in one corner to reveal a criminal's face reflected in the window of a parked car, and designers just shake their heads—not to mention crime lab technicians. If you try to increase the resolution of an image—especially one from a video—you get blur and lots of it. When you "enlarge" a photo or "add resolution" with image-editing software like Photoshop, the pixels are just cloned in all four directions (interpolated is the technical term). So every pixel is padded with identical pixels and you don't really add new data so much as you just spread the current data out. Which is why the photo gets more and more blurry.
Photographs used on web sites don't need to have ultra high resolution, as opposed to photographs used for brochures and magazines where bigger is always better. Usually for a website, images that are 1000 pixels on their longest side are big enough.
But there are other types of digital images that can be enlarged infinitely. The one we most often ask for, especially when we're dealing with logos, is a vector format image. Vector images are made with anchor points and lines rather than pixels so they can be enlarged and reduced with no loss at all.
They are mathematical shapes which are are much more editable than a photo. Pieces can be separated and moved around without any cutting or erasing. Colors can be swapped in several places at once and they are generally much less limiting than pixel-based images. But they also look more simple and two-dimensional than photos.
The most common type of vector file is an .ai (Adobe Illustrator file—our favorite choice when we're designing logos) but -xs.pngs and .pdfs can also hold vector information. If you've had an .ai version of your logo lying around and you didn't know what to do with it, keep it around because all designers and printers in your future will be asking for it. And if you're having a logo created, make sure a vector version is included with your final files.
Learn more about vector images at: http://en.wikipedia.org/wiki/Vector_graphics