Primary meristems are those responsible for primary growth in plants.  Primary meristems are located at the apices (tips) of stems and roots, and in buds on the stems in the axils (upper angles) of the bases of  leaves.  Meristems at the tips of stems and roots are called apical meristems, while those in the axils of leaves are referred to as axillary meristems (or lateral bud meristems).  Root apical meristms are responsible for continued lengthening of roots.  Stem apical meristems are responsible for lengthening of the main stem and producing new leaves and axillary meristems.  The axillary meristems (frequently called axillary buds or lateral buds) are responisble for producing stem branches.