For the sake of anyone reading this but not exploring the articles, High Magic is generally defined as ceremonial, or ritual magic. It is also generally used not for personal game (such as in love, protection, money, etc. spells) but in to contact a higher power and otherwise acquire wisdom. This could be in prayer and communion with one's deity or the summoning and binding of demons or the invocation of angels and a host of other spirits.
Lower magic is generally less formal. It can be energy work, folk magic, or any number of other concepts of magical practice. In this sense most people practice low magic most of the time. Otherwise, it is also generally used to describe all magic seeking to help achieve personal gain or gain for somebody else. Again, this would include love spells, money drawing spells, protection spells... Even healing spells.
Low magic, often without ceremony, seeks to bend the nature of things to achieve a beneficial outcome. High magic seeks to understand the way of things, often through ceremonial ritual.
As in all things, there are grey areas and debates over the concepts.