Five Sankara Mutts and Kanchi Mutt were established by Sri Adi Sankaracharya. As we all know the purpose of Sri Adi Sankaracharya's life was to rally the Hindu religion and give a proper direction to the followers of Sanatana Dharma. Hindu religion and it's principles, at that time was challenged by other off-shoot philosophies. Also Sri Adi Sankaracharya was probably able to visualise at the time the later threats of Muslim and Christian invasion.
The question now, is the purpose and the relevance of Sankara Mutts established by Sri Adi Sankara. First we must understand that these Mutts are supposed to preserve the Hindu religion and not to propagate it, which is a task being well done by these Mutts. One would naturally think that Hindu religion has to be preserved by making the people aware of Hindu values.
So we must reflect upon what constitutes Hindu values. The following are some of the Hindu values that I can readily think of;
Realisation of the principles of Karma and Dharma
Means of conduct of one's life to achieve the life goals (spiritual)
Duties & Responsibilities of an individual in achievement of life goals. This will include the division of society along caste lines. Castes were created purely for facilitating professional duties and not for division of society into higher and lower.
Clear duties prescribed for each caste and it's interchangeability.
Vasudaiva Kutumbakam - the world is one family
To harmonise all things in nature with individuals and to respect & regard every component of the eco-system..
The rites and practices to follow for a layman ( with even a minimum understanding of the religious principles). It should be noted here that subjects were given a wide choice as long as they conformed to the ultimate goal. This is the reason there are so many Institutions for Hindu religion such as Shaivites & Vaishnava traditions, Madhava traditions, Ramakrishna Mission, Sikhism, Swaminarayan cult, Radhaswomi Satsang, Bahai faith etc.
Presently Sankara Mutts have branches in various cities of India making it easier for people to approach them. They run Veda paatashalas, mission hospitals, gaushalas, patronise schools, run colleges, train brahmin priests, conduct upanayanams and marriages for the poor, organise annadaanas, assist temple establishments and so on. The tradition of daily pujas and special day functions throughout the year are all observed in letter & spirit. All these are done to reach out to people and as an example to the people on how to be ideal citizens and contribute to society
May be I can suggest a few more initiatives such as holistic centres in every town and village of India which can provide health dispensaries, teach yoga, have meditation centres, organise satsangs, provide counselling, provide skills in traditional areas such as pottery, handicrafts, sculpting, looming and agriculture, advise people on some wrong practices such as animal sacrifice, drinking, atrocities on women etc. Such efforts will go a long way in raising the awareness among people.
