Guilds are organisations of players working collectively in The Elder Scrolls Online who usually have similar interests and goals. When a guild takes control of a keep or one of its resources, the guild's store and bank are able to be used there via the keep's quartermaster.
Players can join a maximum of 5 guilds per account.
If an account makes a character from a different faction they can still chat in the guild and group up with players from the same faction as their character, but players will not receive the bonuses for any keeps or resources held if they are from a different faction than the guild's starting faction. 
Guild Stores will work in two distinct ways. First, it will allow players in the Guild to sell items to one another internally. Secondly, if the Guild has captured a Keep/Resource in Cyrodiil, there will be an opportunity to sell to guildmates in that keep without having to teleport out of Cyrodiil.
In Guild Stores, players can set their own prices and sell any item they want, provided it isn't bound to their character or an Imperial Edition item.
Since there is no global auction house system in The Elder Scrolls Online, guilds can be created with massive amounts of players for the sole purpose of trading/buying/selling.
Guild Banks are storage areas for the Guild's members. Players can deposit or withdraw items from this bank and the Guildmaster or an Officer is able to control what ranks are able to deposit and/or withdraw from the bank. Anything can be put in the guild bank, regardless if it is bound to your character or not.