The phrase "to embark on an adventure" means to begin a journey or experience that is exciting, challenging and often involves some level of risk or uncertainty. It is typically used when someone decides to take on a new and unpredictable situation, such as traveling to a new place or trying out a new hobby. The phrase can also be used to describe a more personal journey of self-discovery or growth, where the outcome is not certain but the experience itself can be enriching and rewarding.