Minecraft wiki entry for Time-saving_tips, associated text: Maps are useful and can be auto-generated in-game. The catch is that you have to move about your world with the map in hand in order to draw it, and that can be dangerous because it's hard to see where you're going. The solution is to press the F1 key, temporarily removing the head-up display, so that you can see clearly and move at full speed without risk. Another way to get the same result is to press F5 to switch to the third-person view. Pressing F1 again (or F5 twice) will put things back to normal. As of 1.9, you can hold the map in your offhand slot without it taking up the screen.
If your map borders the sea, or if you have a river within reach, another quick (and safe) mapping method is to build a boat and ride in it around the coastline(s) of the area you want to map. The map will extend a reasonable distance inland, and you can 'fill in' any remaining holes in the coverage on foot. You can also move reasonably safely through swamps and the wider rivers.
Unexplored jungle terrain is very hard to traverse quickly. Here, the best practice is to start by tracing the perimeter of the jungle from the surrounding non-jungle biomes. Even swamps and dense woods are quicker to move through than jungle. Only venture into the jungle if it's a big one and you are determined to map every last part of it.
Ride a horse or fly with elytra and fireworks, if possible.