Someone who is harried is feeling the stress of being rushed, overworked, or harassed. A harried parent might be exhausted but still have to make 3 dozen cupcakes for school and help with a science project.
Harried comes from the verb harry, which itself is from the Middle English word herigan, meaning to pillage, plunder, or make war. Today, harried doesn't imply an act of war, but rather someone who is frazzled or a situation that might cause that feeling. If the project you're working on has been harried from start to finish, you'll be lucky to keep your sanity.