The "Dogs" are businessmen who use their power to make themselves richer and more powerful at the expense of others. At the end of the song, they get old and fat before dying of cancer.
Around 15:30 into the song, Roger Waters says: "Who was trained not to spit - in a fan." Although it is probably a coincidence, Waters once spit at a fan. Pink Floyd performed at a concert in Montreal, and when a fan tried to climb onto stage, Waters hocked a loogy into the guy's face. This gave Roger the idea for the movie and album The Wall -in an interview he said that the event created a barrier or a "wall" between them and the fans.
This was the only song on the album not written solely by Roger Waters. David Gilmour wrote all the chords - the main music part of it. And the two together wrote some other bits at the end.
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