According to this paper by Barello et al in the Journal of Participatory Medicine, the muddled answer depends on when it was used as well as your professional background.
Using a densely written "lexicographic qualitative analysis" to dive into over 250 scientific papers, the authors found that the term has evolved and may still be in its infancy. When it first began to regularly appear about 15 years ago, the term "patient engagement" was used in behavioral and nursing contexts to describe a dimension of established one-on-one provider-patient care. Since then, it's been used in a biomedical sense to portray a new relationship between a system and a patient.
The authors point out that how "engagement" is achieved depends on a spectrum of patient perspectives that range from unaware to really motivated. The Population Health Blog suggests that one way to think about it may be the transtheoretical "readiness to change" model.
The one thing that has been missing in the scientific papers is the patients' perspective. Ironically, no one has asked and cataloged their answers in any systemic manner.
Last but not least, it's unclear if real purpose of achieving patient "engagement" is greater autonomy, relationship-building, making health care more responsive, reducing costs, or improving public health. As a result, it's a catchphrase has become all things to all people.
While this lacks the all-important input of folks like this and may also be an exercise in tautology, the Population Health Blog managed to extract something of a definition for the term: a span of cognitive processes that seeks participation, compliance, learning and self-management in health care, including disease, prevention and health.
Image from Wikipedia