A party is two or more players that have chosen to be part of the same group. Being in a party allows for useful things such as party tracking, split fame from killing creatures, party chat, the ability to loot each other and each others creatures and much more.
Creating a Party
Type /add and target the person you wish to add with the cursor that appears. or Single click on the person to obtain the menu, select 'add party member'
Joining a Party
Type /accept to join a party.
Leaving a Party
Type /quit or single click yourself and select the appropriate menu option.
The party menu can be accessed by the second scroll inside of your Paperdoll. Double clicking it will reveal a menu allowing you to perform certain party actions, such as kicking.
Each party member has a red and green dot to heal or cure them by clicking in the button (assuming you have a spell that does this).