Homeschooling" is probably the most common term currently in use to describe parents taking direct responsibility for their children's education instead of sending the children to school. Other phrases used include: home-based education, home-based learning, family- and community-based learning, homelearning.
There are a number of different approaches that can be taken by homeschooling parents according to their values, beliefs and personal styles and also according to what works for their own individual children. On the spectrum between structure and freedom, at one end there is the structured approach of "school-at-home" in which the family follows a grade-based curriculum using textbooks and worksheets, and at the other end of the spectrum there is what is sometimes called "unschooling" or "child-led learning," which is more informal and integrated into daily life. There are also approaches in-between these two poles, that combine structure and natural learning in different measures, and for each of all these approaches there are variations according to the family's values and beliefs and particular philosophies of life.
It's up to you to decide what form homeschooling will take in your own family. We recommend you find out more about the different approaches before settling on one. You may find, as well, that your approach changes over time as you respond to the needs and interests of your children and the logistics and economics of providing for their education at home. For further exploration of your options, please see the question "How do I decide what approach to take?" and visit our page on Teaching Methods and Learning Philosophies.