High-Resolution Images are very important
When designing custom shirts, most people use their own images which they upload onto their design. This image may only be part of the design, or it may even be the entire design itself. Regardless, if you want that image to appear clearly on your design, make sure it is high-resolution.
What does "High-Resolution" mean?
Basically, the most popular image formats (jpg, gif, png, bmp) make the image a raster image. This means that the image is composed of a finite number of pixels, or tiny dots which represent a single solid color each. The smaller your pixels your image uses, the more pixels it uses. Keeping the image's size constant: the more pixels it uses, the greater the resolution and quality it has.
Typically, the higher-resolution an image is, the greater its file size will be.
Remember that images that you expand will lose quality, and images that you shrink (not all the time) will gain quality. Thus, the bigger your images are, the better overall resolution they will have when placed on your shirt.
If you need help choosing your image, check out some tips about artful custom shirt designing.
To go more into how images are processed before being printed on your custom t-shirt...
After you submit your image, most custom shirt companies will convert your raster image into a vector image. This means the image will be composed of geometric properties like lines instead of pixels for infinite resizability. However, if your original raster image is of poor quality, then it's converted vector product may turn out skewed and distorted. For example, if your original image has text in it but is poor resolution, then the vector image produced out of it may make the text look squiggly and undefined.
Shirt Printers use the vector image as the basis of your design to print on your shirt.
A note about digital prints:
People commonly use real-world photographs if they plan on ordering custom t-shirts that require digital printing. These photographs often have gradients, or shadows of colors inside them. Gradients are difficult to vectorize, and as a result require very high-resolution images to produce a crystal clear print out of. If you plan on using a real-world photograph, make sure its image is of excellent quality.
More about printing can be found here.
Pay attention to how much detail your image requires. If it's a snapshop of a messy room, it will require a lot of detail (and thus require a high-resolution image). If it's a simple polygonal drawing that only uses a few colors, it won't require as much detail.
Good custom t-shirt companies will usually tell you if your image isn't high-resolution enough. My favorite would definitely be ooShirts.
Hope this helps, thanks.