Shaped Maps are upgraded versions of regular maps on the Atlas in Path of Exile, and a shaped map will always be 5 levels higher than the original. In order to shape a map you need to find a Shaper's Orb. These will drop upon completing the bonus objective on specific maps, starting at level 6. In the cast of the level 6 one, a Shaper's Orb will drop when doing the bonus objective in the Spider Forest Map. You can see all the maps that drops these by going to the Atlas and look for map areas with a big blue circle around them.
The Shaper's Orb will only drop the first time you complete the bonus objective, and there is one Shaper's Orb for all the tiers. Base level tier 1 - 7 had one Shaper's Orb each, tier 8 got 2, while tier 9 and 10 has 3 Shaper's Orb each.
Each Shaper's Orb can only be used on one map, so you have to pick which you you prefer. If you for example pick Jungle Valley for tier 1, you cannot get a Shaper's Orb to upgrade the other 3 tier 1 maps. However, you can trade 5x Orb of Regret + 20x Cartographer's Chisel to get an Unshaping Orb, which lets you switch which map to shape. This is pretty expensive, you it is better to pick the one you want to begin with.
Once you have shaped a map, a shaped version of the map can drop from appropriate tier maps, so when you shape a tier 1 map into tier 6, the shaped version of the map can drop from level 4-6 maps and above. However, if you have any remaining tier 1 versions of the maps, these will take you to the regular unshaped map.