When characters are in a party they share experience, benefit from certain auras, and are able to use each other's town portal. There are other benefits as well. You can experience all of this for yourself on a Bardo Safari.
When you enter an online game there will typically be other characters in the game. Playing with others is the chief advantage of playing online. The place to invite and accept invitations to "party" is on the "Party" screen.
To access the Party screen press the P key.
In this case there is one other player in the game by the name of LarryTheWolf. Larry is a level 28 druid. This you can tell even without being in the same party. To invite Larry to "party up" click on the "invite" button.
This information popup window confirms that to invite a player to join your party you press the "invite" button. This is not rocket science folks. The game is made for preteens to figure out.
After you press the "invite" button, it will change into a "cancel" button. If you want to cancel an invitation you would click on this button.
When (and if) Larry accepts the invitation to party up, his information line will turn green. Now you can also tell where in the game the players in your party are located. In this case, Larry is in Cold Plains.
Let's assume that upon entering a new game you see a message appear on the screen such as this.
To accept an invitation to join a party screen press the P key.
Here you see the "accept" button. To accept an invitation to join a party, press the "accept" button.