Clans are players who group together for survival. Being in a clan can be very advantageous in the harsh environment that is HCSMP.
In the beginning, in the time before PvP, people gathered together in the comfort of the Reddit Community Center, and no clans were needed. After it's destruction by Charker and others, people separated off, and once PvP was turned on, regularly formed warlike factions.
Clans often share some or all of their resources, help each other out, build together, and go raiding together. Although this may sound like a happy time, establishing a clan and inviting new members can be fraught with danger - people have been know to backstab their clan members. Trust no one.