What is mental health?

Freud summarized mental health as the ability to love and work. The WHO definition is a bout a page long and essentially says the same with the addition of 'play'.
The definition I use then is that Mental Health is the ability to love, work and play.
Love was best defined in a little book called the Art of Loving by Erich Fromm.  In that book he summarized the development of the thinking about love over history separating falling in love or lust from standing in love or adult love.

Love is not a scientific term. The term "attachment" is the word used in research for our principal relationships.  These first refer to the relationships we have with our parents and brothers and sisters and extended family, blood relations.  The term love also refers to our relationships with friends and others less closely related to us in our  community. It's that whole emotional interconnected world of relationships that at it's highest has been described ideally as our relationship with our 'higher power' or God, for lack of a better word.  As well given the golden rule of "love your neighbour as yourself" or "do unto others as you would have them do unto you", it refers to our love of ourselves in the healthiest sense of that.

Work refers primarily to our contribution to the community.  This is predominantly defined as work that in our society translates directly into money. The community as a whole attributes a monetary role to different work. Individually I may feel that my working on my guitar playing is 'work' however society has said by its basic reimbursement that it is willing to pay Keith Richards for this work but to date has never paid me enough that I could be self supporting.

Adults to the best of their ability cooperate in society and work to be self supporting.  Work is humbling in that it usually means service to another and doing what I might not necessarily want to do at any particular time.  Even great artists might rather run through the sprinkler than practice violin but if they did just that they would be less likely to succeed in their work.

Volunteer work is work which though like work doesn't get 'paid' but serves the community and involves cooperation and factors of reliability and responsibility. Philanthropy and charity are examples of volunteerism.  They are considered altruistic rather than narcissistic.

Self care is a kind of work.  To date communities have been loathe to pay for self care because it's a fine line between the basics of self care and self pampering.
In the area of work, subjectivity and objectivity are always an issue.  Tom Sawyer contains a story about work being made to be fun.  Work doesn't have to be painful but it's always inherrently a 'service' to others and 'valued' by community. Many a golfer would call what he is doing 'work', like those who 'play' on the computer or doodle.  They may even present a long face and seek to elicit pity from those around them. The word "billable hours" came to be used in the workplace to address "slackers" no matter what their story.

In contrast play is all that leisure entails.  It's part of a balanced life. It's rest and recreation.  Society doesnt' pay individuals to play though there has been a controversial movement in this direction with state bought call girls being supplied for the disabled in some european districts.  Workaholism has been idenfitied as such a 'disease' because it has a short shelf life and may lead to significant individual and community dysfunction. Even military studies show that a balance of work and leisure results in better productivity.

Mental illness is defined as dysfunction in work, social or leisure activity as a result of a predominantly mental or emotional or cognitive cause, Commonly physical illness is associated with accompanying mental illness. Often the physical illness presents as a depression or even a psychosis.  Addictions present at first a mental illness with work usually being last effected since it supplies the habit but eventually addiction will lead to a variety of physical illness.

Mental Health is also disease prevention.  WHO studies of longevity showed that people who lived longest worked and had a purpose in their community as a consequence of this contribution.  Isolation is associated with misery and those who are happiest have a close relationship with family and friends.  Maintaining friendships and family relationships often requires effort just like showering and doing laundry can appear onerous at times. This persistence in face of lack of immediate positive reinforcement is one of the positive psychological strengths that Seligman addresses in his studies of Authentic Happiness.
Leisure involves exercise. There are no obese people over 100 years of age.  Exercise and leaness, especially measured by waist size are associated with good health and longevity.  Longevity without quality of life isn't a particularly attractive destination.  The Nun studies showed that those who were least likely to develop dementia were those who remained socially interactive and continued to learn and participate in community.

Mental health isn't all that much different from overall 'health' and certainly good physical health depends to a large degree on the recognition of the interaction between body and mind.
Psychosomatic medicine is the modern and postmodern approach to all disease that says that body and mind aren't separate but work together.  The toe bone is connected to the head bone. Good physical health and good mental health work together contributing to each other.