Tibia is strongly based on the community and one's relations with others. Guilds strengthens one's relations with others in the world.
The guilds could be organized guilds made to bring wealth to their members (eg. Mercenarys), to help other players (eg. Alliance of Justice, Loremasters, Rising Dragons (Secura/Amera/Antica)), or just as a family or group of very good friends (eg. Castlings, Henceforth Family, Crimson Chaos).
To join a guild, first go to the guilds page and select your world. Then, scroll down to and select the world in which the invited character resides. Afterwards, find the guild and select the view button on the right and enter the guilds page; once in the guild page, select the 'Join Guild' button. As a sidenote, you must be logged into your account to join the guild.