The Shape of Things
Note: Shaped maps should not be confused with Shaper-influenced maps. The two mechanics are entirely separate and, admittedly, a bit confusingly named.
After you complete some of Zana's quests relating to the Shaper and the Elder, she'll reward you with a Shaper's Orb. Shaper's Orbs can be used to convert one map of a particular tier on your Atlas into a version of the same map five tiers higher. For example, a Shaper's Orb (Tier 1) can convert Lookout Map (a Tier 1 map) into Shaped Lookout Map (a Tier 6 map).
This does not affect existing copies of the map in question. In this example, your existing Lookout Maps would remain Tier 1 - but you would now be eligible to find Shaped Lookout Maps when maps drop for you in the wild and would no longer be eligible to find the regular Lookout Map.
Shaper's Orbs are not quite permanent - it is possible to un-shape a map and recover the orb - but doing so is quite expensive. As a result, you should choose your Shape targets carefully.
But Why Though?
Shaping a map has a few benefits.
One, it allows you to upgrade a map with a layout, boss, or Divination Card drop that is of particularly high value to you. For example, maybe you're playing a build that thrives in open areas; you might then choose to Shape a map with a wide-open layout. Or suppose you're trying to farm a Divination Card for a particular valuable or interesting item; you might Shape a map that drops it so that you'll get better loot from it.
Two, it allows you to place higher-tier maps near lower-tier ones, meaning they can be affected by cheaper low-tier Sextants. For example, a shaped Tier 6 map (which becomes Tier 11) can be in range of a Tier 4 map that only requires the lowest tier of Sextant, making it far easier to sustain Sextant effects on the higher-tier map.
Three, it can play a part in map drop manipulation by allowing you to remove a certain map from the drop pool. In advanced Atlas manipulation strategies, this can be used to help force drops of specific desirable maps.
Four, it can allow you to increase your odds of facing the Elder or his Guardians in high-tier maps if you're manipulating the behavior of Elder influence on your Atlas.
The Elder Orb
At the very end of the Atlas, you'll also be rewarded with an Elder Orb. This special, one-off orb upgrades any map on your Atlas to Tier 16, the highest tier possible for a normal map, regardless of its original tier.