Concealment is a new mechanic introduced in XCOM 2. In certain mission types your squads will start concealed, which means that the enemy won't be aware of your presence, and will patrol the map without knowing precisely where you are. This mechanic allows setting ambushes; to set an ambush just distribute all your soldiers in good cover and put all except one in Overwatch, then use the last soldier to attack, this will break concealment and hell will break loose-- though be aware that any survivors may then be primed to counter-attack. Attacks from concealment will not have the penalties normally associated with Overwatch, particularly there is no aim penalty, and the shots can crit (which they will do often, since ambushed enemies are usually not in cover).
It is effectively impossible to full stealth a mission, as either you will need to clear the area of enemies, or the site of an objective will be camped by an alien pod: even if you get close, doing the required action will reveal you. The only Concealment-centric Achievement is to simply set up an ambush.
Normally, the area shown around a patrolling pod is roughly the movement range: remaining outside this range will usually ensure that you won't be spotted in the next movement. However, one Dark Event, Vigilance, increases the Alertness radius of enemies while in concealment mode (but won't increase movement range).
Attacking is the most obvious way of breaking concealment, but that is not the only thing that will break it. Moving while too close to an enemy or civilian will break concealment too (though if en enemy moves close to your soldier, they won't detect them if they remain still). A patrolling enemy flanking you will reveal your squad: they will also get a free shot on the flanked soldier. Also, running through windows or doors breaks concealment; but if you take cover next to a door first, you're allowed to open it without breaking cover. Finally, failing a hack will reveal your squad.
Normally, if one soldier breaks concealment for any reason all others in the squad will be automatically revealed. The exception to this is Rangers with the Phantom perk.
Getting most of Concealment
There are certain skills that can be used to boost the effectiveness of Concealment. Rangers excel with Concealment, their first three Scout skills improving it. Phantom allows the Ranger to remain in concealment after the rest of the squad is revealed, allowing them to be an advance scout all mission (it also causes the Ranger to start in concealment on missions that normally don't). Note that Phantom means the Ranger won't be revealed when the rest of the squad ambushes, which means they won't fire. To have a Phantom Ranger take part in an ambush, have them take the triggering shot. Shadowstrike gives the Ranger a considerable boost to Aim and Crit when attacking an enemy that is unaware of them, which most usually happens when concealed. Conceal allows the Ranger to enter Concealment once per mission.
Sharpshooter´s Kill Zone and Grenadier¨s Saturation Fire are good abilities to use with an ambush, since enemies will be out of cover so you will have the bonus to Aim and Crit with each shot when attacking with those AoE skills.
Enemies have reduced Hack Defense while your squad is undetected. This makes shutting down mechanical enemies before you strike relatively easy (though failing the shutdown attempt will reveal you).