The phrase "to embark on a new adventure" means to begin a new journey or experience, often involving some level of excitement and uncertainty. It can refer to starting something completely new, such as traveling to an unfamiliar place or trying out a brand new hobby, or it could mean taking the first steps towards achieving a long-term goal or pursuing a dream. The phrase suggests that the person is entering into a fresh and exciting chapter in their life, full of possibilities and opportunities for growth.