A mutual option is an optional year at the end of a contract. In order for the optional year to become guaranteed, both parties must agree to exercise the option.
Mutual options are very rarely exercised. If a player enjoys a strong season, the club will often exercise its half of the option in the hope of retaining the player on a one-year deal. However, the player, fresh off a high-quality performance, will likely wish to test the open market in search of a larger guarantee on a one-year or a multi-year contract. Likewise, a player whose stock is down might exercise his half of the option rather than test free agency, but his club may no longer view him as worth that salary.
Though rare, the mutual option has been exercised in the past. Planning to retire following the 2015 season, Aramis Ramirez agreed to exercise his half of a $14 million mutual option with the Brewers. Perhaps viewing $14 million as a fair salary for a player of Ramirez's ability, Milwaukee exercised its half of the option as well.