Archon Shards were added to Warframe with the Veilbreaker update, and they are more or less a way to add an extra bit of power to your Warframes.

Archon Shards can be installed on a Warframe of your choice via a new segment that you will get as a reward for completing the Veilbreaker quest.

The shards provide you with the option to increase your Warframes stats (ex health, shield, health regen, etc.) depending on which of the 3 types of shards you use.

Every Warframe can currently have up to 5 Archon Shards installed at any given time.

The fastest and most reliable way to get Archon Shards would be to complete Archon Hunts, as they have the same rewards as Sorties, but with a bonus reward of a guaranteed Archon Shard.

Here is a guide that will go more into detail on Archon Shards: