Colosseum is a virtual battleground, where you can test yourself against different monsters and bosses. There are two modes, and three different levels, which you unlock at 30, 40, and 50. The two modes are solo and party.
For Solo Colosseum, you enter by yourself, but you can have 3 Astels summoned at any time, whether they are Servants or Guardians. This allows you a large amount of flexibility and available strategy for the fights you will face. In the middle of the Colosseum Arena, there is a giant crystal. Protecting this crystal is the key to success in Colosseum. As waves of mobs approach, you will want to burn them down before they can harm your crystal, but you must balance this with the power and damage output of your Astels. You will face several waves of monsters, followed by a boss, for five rounds. Your rank will depend on your speed and the health of your crystal.
Party Colosseum is much like solo Colosseum, except you can enter with 4 players, but cannot have 3 Astels out at a time. You still will fight waves of monsters, followed by a boss, and the health of your crystal will help determine your rank at the end.
You will receive 2 Colosseum tickets per day, and each Colosseum run will consume 1 ticket. There are also dailies and weeklies you can do for further rewards for your completion of Colosseum.