The center of symmetry i is a point in space such that if a line is drawn from any part (atom) of the molecule to that point and extended an equal distance beyond it, an analogous part (atom) will be encountered.
An example of point of symmetry is 1,3-trans-disubstituted cyclobutane, below. Note that the chiral G substituent is inverted on both sides of the point of symmetry. This symmetry element is sometimes also called "the point of inversion".
Point of symmetry placed at the origin of Cartesian coordinate system converts point A(x,y,z) into A'(-x,-y,-z). Molecules which have a center of symmetry are achiral, even though they may have chiral fragments in them.
Planes, centers and alternating axes correspond to "symmetry operations of the second kind" or "improper operations" since they bring into coincidence the material point of an object with its mirror reflection.
A plane of symmetry 
is a reflection
plane which brings into coincidence one point of the molecule with another
one through the mirror reflection.
In contrast to the center of symmetry, a plane of symmetry converts A(x,y,z) into A'(-x,y,z), A'(x,-y,z) or A'(x,y,-z), depending which of the cartesian planes, yz, xz, or xy, respectively, is a plane of symmetry.
A plane of symmetry precludes chirality, i.e. molecules featuring
are achiral.
Examples of molecules with a plane of symmetry only:
Most aromatic drugs without attached chiral chains have only a plane of symmetry.
Examples of molecules with a plane of symmetry and n-fold perpendicular axis of symmetry:
Symmetry axis Cn, also called n-fold axis, is an axis which rotates the object (molecule) around by 360ø/n, such that the new position of an object is superimposable with the original one.
For example, 1,3-substituted cyclobutane has a twofold axis C2 and the cis-tetrasubstituted cyclobutane has a C4 axis. The presence of the Cn does not preclude chirality. Chirality, therefore, can not be equated with total asymmetry.
The 2-fold axis C2 changes the sign of two coordinates only, e.g. the axis that runs colinearly with the z axis converts A(x,y,z) into A(-x,-y,z).
Examples of molecules with an axis of symmetry only:
Examples of molecules with axis of symmetry and a coaxial plane of symmetry
