Mimic Beacons can be tossed into an open area, without any cover, to provoke the enemy into targeting the temporary holographic target instead of one of your other soldiers. In most cases the enemy will then waste a turn killing the hologram, which appears to match the health of the user who threw the beacon.
If the hologram is destroyed before the enemy turn ends, any hostile units that have not attacked will still be free to target your soldiers.
Thrown exactly like a grenade, but can't be shot from a grenade launcher.
The hologram seems to match the soldier who throws it in appearance.
The hologram can not take cover.
The hologram has fixed 12 HP (on Legendary difficulty)
Mimic Beacons are an incredibly powerful tool when used correctly. The ability to "panic button" a beacon when something goes wrong can allow for riskier moves (a skullmining or evac) as well as providing a means to escape a situation that has gone horribly and dreadfully wrong.
A Mimic Beacon thrown outside of cover will generally see the enemy focus it down. Especially in later parts of the game, its generally somewhat difficult for a single pod to kill more than one full-HP soldier: the beacon itself.
Beacons are expensive, but your supply is primarily limited by Faceless Corpses, which are somewhat rare. It is therefore highly recommended that you do the following
Never Sell Faceless Corpses on the Black Market.
Win Retaliation Missions (though you probably want to be doing this anyway).
Allow the Faceless Dark Event to Fire
Faceless are generally the weakest enemy in XCOM, and are unlikely to really throw a game away like some of the other events.
Mimic Beacons, once you realize their power, will be incorporated into your tactical decision making. In the event that your carrier goes down, this might seriously undermine your plans and overall resilience of the squad. Having a back up ensures that losing one does not seriously degrade your tactical situation.
On most missions, where there are roughly 4+ pods, you imagine the following. 1 Pod is iced from concealment. 2 Pods are taken out with the help of mimics (if necessary), leaving only one Pod where you could conceivably have to take most of your wounds. It would be extremely difficult to mess up that badly.