Apical Meristems
Apical meristems are those located at the tips of all stems and roots. The system that involves the shoot, meristems and involucral leaves is called a bud. Apical meristems cause tip growth: a defining feature that differentiates plants and animals. Whereas animals grow somewhat proportionally, then cease to grow once reaching a final size, plants will constantly grow from the tips. In the case of a damaged flower or leaf, entirely new organs grow rather than replacing or repairing the damaged parts.
Lateral Meristems
Many plants and tree species have lateral meristems. These meristems are located in the cambium, the vascular cambium and the cork cambium and cause growth in girth. This process, also called secondary growth, is the primary cause of the annual rings you see when a tree is cut down, as this growth seldom occurs all year. The thickening usually occurs when the weight of new branches threatens to break the tree, which synchronizes with the growth of these limbs during certain times of year.
Intercalary Meristems
Intercalary meristems are located in tissue that is more or less differentiated, usually at the base of each internode. This fact is interesting because the species of plants with intercalary meristems have the ability to revert from a differentiated state back to a merismatic existence, allowing changes and division under new circumstances or proceeding an important change. This ability is exploited by cuttings and grafting in horticulture.
Primary vs. Secondary Meristems
Apical meristems are classified as primary meristems because they contribute to primary growth, that is, tip growth. Lateral meristems are classified as secondary meristems because they contribute to girth growth, or secondary growth. Because intercalary meristems are so rare, they don't occupy a place in either of these classifications. Thus, the two most common types of meristems are classified basically for the layperson by the direction in which they cause the plant to grow -- either up or out.