Invagination means to fold inward or to sheath. In biology, this can refer to a number of processes.
(1) Invagination is the morphogenetic processes by which an embryo takes form, and is the initial step of gastrulation, the massive reorganization of the embryo from a simple spherical ball of cells, the blastula, into a multi-layered organism, with differentiated germ layers: endoderm, mesoderm, and ectoderm. More localized invaginations also occur later in embryonic development, to form coelom, etc.
(3) Invagination in some bacteria (also called a mesosome) is a tightly-folded region of the cell membrane containing all the membrane-bound proteins required for respiration and photosynthesis. It can also be associated with the nucleoid.
(4) The inner membrane of a mitochondrion invaginates to form cristae, thus providing a much greater surface area to accommodate the protein complexes and other participants that produce ATP.
In development biology, dosal part of cells can inergrate adjacent cells into invagination. No matter what cell it is.