A lattice is a (idealized) structure of crystals where each lattice point represent an identical group of atoms. A group is sometimes called a basis. One can form basis vectors with which all lattice point positions can be expressed. The unit cell (I guess you mean the primitive cell) is the volume defined by the set of basis vectors. This is the smallest volume; there are no cells with smaller volumes. Hopefully this was of help. If not, don't hesitate to ask.
my textbook says: unit cell: crystal structure that's the smallest group of atoms possessing the symmetry of the crystal lattice: orderly array of points in space so does that mean that the unit cell is part of the lattice?