Comments

Comment by Nerrevar

Killing mobs under the Sentinax ship rewards Broken Sentinax Beacon, Which starts the quest The Shadow of the Sentinax Turn this in to Captain Ruysantos at Deliverance Point. You'll then be introduced to the various items you can buy with Nethershards.

Related Items
These beacons will create portals that summon progressively more-challenging demons:

Uncommon Beacons:

Rare Beacons:

Epic Beacons:

There are also some beacons with profession benefits:

Sentinax Beacon of the Bloodstrike: Commands the Sentinax to fire a Bloodstrike at your current location, unearthing Blood of Sargeras. Deals 150% of maximum health as Chaos damage.
Sentinax Beacon of Petrification: Commands the Sentinax to fire a Petrum beam at your current location, turning everything in the area to felslate.
Sentinax Beacon of Fel Growth: Commands the Sentinax to fire a Fel Seed at your current location, causing starlight roses to rapidly grow.

Comment by Haqin

Quick summary:

Can be looted from mobs under The Sentinax or, for a much better drop rate and often in multiples, from the Broken Shore rares that show up on your map.
This beacon, when used under The Sentinax, will summon 2-3 demonic portals that spew forth Sentinax Observers, Legion Painmaidens and Sentinax Interrogators.
They have a chance to drop Sentinax Beacon of Greater Torment which will create Empowered Torment portals, spewing forth elite mobs.
Only one set of 'Torment' portals can be open at a time, using a beacon while one is already open will extend it's duration. If the portals are Empowered, an uncommon beacon will still extend it's Empowered duration (which is useful!)
The elite mobs from the Empowered Torment portals have a chance to drop Portal-Stone: Illisthyndria

What's The Sentinax?
The Sentinax is a Crusade Ship that moves about the Broken Shore, you'll be able to see it on your map. It stays above different areas of the zone for 3 hours, then moves on.

When you are in the area underneath it, you gain the buff The Shadow of the Sentinax. Killing creatues while having this buff gives you a chance to loot one of the uncommon Sentinax Beacons. The first time you do this you'll get a Broken Sentinax Beacon, which gives an introduction quest to the Sentinax concept. I got my first uncommon Beacon from the same mob that dropped the quest item, so it seems you don't need to have done the quest to start looting Beacons.

The drop rate from these mobs can, at times, seem frustratingly low, so look to kill the rare spawns around the Broken Shore, which always drop one or more.

Using one of these Beacons causes 2-3 portals to open up around the area and spew forth a few waves of mobs. Once the waves are defeated, the portal closes.

Rare versions of the beacons, like the one linked above, can drop from the mobs that come through these portals, which create Empowered portals. These spew forth Elite mobs that have a chance to drop Epic Beacons, which summon Demonic Lieutenants.

So, what's the point of all this Beacon looting? Well it's primarily a design to make farming Nethershards a little more interesting. There are also a couple of related achievements though: Bringing Home the Beacon and Naxt Victim. You will also need to farm a few demonic lieutenants for the quest Mark of the Sentinax.

Edit: For extra info and clarity.