Pictures on computers are stored in two basic forms - Bitmaps and Vectors. A Bitmap file consists of many points (called pixels) that can be any colour. Vector files on the other hand are specifications of lines or curves that when drawn and filled form a picture. Trace is a program that can convert bitmap images into vector form.
There are advantages and disadvantages to both types of file. Bitmap files use a lot of memory and can't be easily scaled. If you attempt to make bitmap files larger they will develop jagged edges. Similarly such 'jaggies' will show up when the image is printed on a high resolution printer. Vector files have no such limitations.
Vector files are usually easier to edit than bitmaps, this is because the curves in them represent whole objects, in a bitmap file individual pixels have to be edited.
A typical bitmap file format is the Windows .bmp file which you can edit using Windows Paint (and many other programs). A typical vector file is the Windows Enhanced Meta file .emf. Again there are many programs for editing these such as Adobe Illustrator, Microsoft Word and Windows Draw. Trace will convert .bmp files into .emf format.
There are limitations to tracing. Trace can only handle bitmap files with 256 colours or less. Bitmaps with more colours tend to be photographic images, this is the type of image which bitmaps are better suited to handling. Not every traced image will be perfect, sometimes simple editing will improve results. Your favourite bitmap manipulation program will allow you to convert images with more than 256 colours to 256 colours or less.