The 13 assassins plan to attack Matsudaira Naritsugu while his journeying to Edo (the old name for Tokyo). In the Edo period the lords of Japan had to travel and stay in Edo. This was called Sankin-kotai, or official journey. The lords stayed to show their loyalty to the shogun and the system helped the shogun keep tabs on the lords.
The trivia item below may give away important plot points.
Out of the 13 assassins, only two survive the final battle: Shinrokuro and Koyata. Both men were not part of the original 11 who chose to take on the mission but in fact either joined as they were about to set off (Shinrokuro) or joined on the way (Koyata).