As part of a guild, you can play together with friends, or make new acquaintances and forge alliances with other players. Being part of a guild makes trading easier, and as a member of a guild you have access to a guild forum, guild chat and more than anything else: you can join war and fight for your guild on the guild continent map!
You will often find that within a guild, players are very helpful, and will come to visit to polish your cultural buildings regularly (which means fewer buildings are necessary for enthusiastic population). Fellow guild members will usually trade with you at reasonable rates. Of course, they will expect the same thing from you.
Go to "Your Guild" tab in the "Global" menu. That's the place where you can see if you got invited to other guilds. If that's the case, you can join a guild which is to your liking. Of course you can also create your own guild and become its chief. To do that, just enter a name for your new guild and you're done! You might want to update coat of arms and description of your new guild to make it more appealing. There is a tab for that called "Administration", and that is also the place from which you can invite other players.