When it comes to CPUs (Central Processing Units) for the home desktop, AMD and Intel are the dominant choices. It may not be clear at first which choice is best for your purposes, but there are several ways in which they differ.
Breadth of Lineup
Intel arguably offers a larger variety of CPUs, from netbooks, laptops, servers and desktops. AMD competes in each space, but Intel is particularly more popular with netbooks.
AMD's CPUs have had a historical reputation for being more aggressively priced than Intel's. It is not unusual for them to introduce a new type of CPU in market segment at a cost much lower than Intel's comparable options.
Cost aside, Intel tends to have the upper hand, partly because they introduce new types of CPUs at a greater rate. They have a larger research & development (R&D) department that allows this.
Intel's Atom CPUs use about half the wattage of AMD's comparable parts, which directly affects the battery life of your laptop or netbook.
Intel CPUs tend to run cooler, making them more enticing for enclosed spaces like laptops and rackmount servers.