Electron orbitals can be defined as the pattern describing the behaviour of an electron within an atom or molecule. More accurately the orbital describes the area in which there is a high probability of an electron being located.
There are two types of electron orbital - atomic or molecular.
Each orbital can contain no more than two electrons, so there are many subdivisions of atomic orbitals to make room for all the electrons within an atom.
These are known as the s, p, d and f orbitals. S orbitals are the primary way in which electrons are displayed and another s orbital can be added at each electron shell. The s orbitals have a spherical orbit. P orbitals are formed in a dumbell shape (two ellipsoids facing each other) and there can be three p orbitals per electron shell. These p orbitals will be perpendicular to each other on a 3D axis.
There may be 5 d orbitals in later electron shells and 7 f orbitals in some. These types of orbitals have highly complex shapes.
These are when two or more atomic orbitals combine to show the possible location of valence electrons within a molecule. There are many forms of molecular orbitals including sigma and pi bonds.
Sigma bonds are formed by the combination of an s orbital with another s orbital, an s orbital with a p orbital or two p orbitals joining end on. Similarly pi bonds are formed by the combination of two p orbitals 'sideways' on.
Single covalent bonds are generally formed by the presence of a sigma bond whereas double bonds are composed of one sigma bond and one pi bond, and triple bonds are composed of 2 pi bonds and a sigma bond.
There are other types of molecular orbitals as well such as delta orbitals which are highly complex.