A canvass is a poll, usually a political one. Around elections, political parties often canvass particular neighborhoods, looking for votes and trying to measure the pulse of the people.
You might think of canvass as the heavy cotton cloth that is pronounced the same although spelled with only one s, that is, canvas. Canvas is used to cover things, and a canvass serves the same sort of purpose. Before elections, politicians want to cover their neighborhoods and districts with canvasses, campaign workers, flyers and the like in hopes of securing votes.