Artifacts are structures built on stars that provide certain bonuses to the empire owning that star. An empire can only build one artifact in it's life, other artifacts must be captured to use them.
Here's the current list of artifacts as of November 2016:
Weapons Platform Edit
This gives a significant boost (equivalent to 2 tech levels) for attacks either against this star itself, or attacks from this star to an adjacent enemy star. It also triggers a fancy animation.
It may also defend from other items, such as missiles or space oddities ...
Wormhole Disruptor Edit
This temporarily (on average about half the time) disrupts the wormhole connecting this star to neighbours. This means that it is protected from attacks (though not empire-wide events), and also that it can not launch any attacks.
It can also have the interesting side-effect of splitting up the galaxy into different isolated parts, which can have some nice effects.
Lunar Monument Edit
This is just an ego-boost for the ruler of the empire, but has no in-game effect (though I have some ideas!).
Research Laboratory Edit
This artifact makes the planet research at a massively increased speed.
Missile Station Edit
Launches fabulous missiles at enemy stars. Fun fact: They can actually hit ships as well, though they never aim at them.
Mind Control Hub Edit
Dispatches Mind Control Pods to nearby stars, to convince them to join the cause of the empire who owns the Hub.
Fleet Base Edit
Hosts 4 Interceptors, that can launch against any hostile ships (or meteors etc) that approach.
Stellar Forcefield Edit
Shields a star providing defense bonuses and destroys all hostile projectiles and ships.
Disrupt Launcher Edit
Shoots Disruption missiles at hostile stars that disable them for a time.
Financial Center Edit
Increases wealth of nearby friendly stars.