Exocytosis is a process in which an intracellular vesicle (membrane bounded sphere) moves to the plasma membrane and subsequent fusion of the vesicular membrane and plasma membrane ensues.
Many cellular processes involve exocytosis. For example a few of the processes that use exocytosis are:
secretion of proteins like enzymes, peptide hormones and antibodies from cells.
turnover of plasma membrane
release of neurotransmitter from presynaptic neurons
placement of integral membrane proteins
acrosome reaction during fertilization
antigen presentation during the immune response
recycling of plasma membrane bound receptors