I'm not sure what level of answer you are looking for - the one above is fine, but here's a less sophisticated one.

Consider a dipole made up of a positive and negative charge separated by a small distance. If you make these charges swap positions, backward and forwards then you have an oscillating electric dipole that will generate electromagnetic waves.

Now consider a small conducting loop and pass a current through the loop that goes one way around and then the other. This is called an oscillating magnetic dipole and also produces electromagnetic waves.

In certain circumstances, an atom (or molecule or nucleus) can behave like an oscillating electric dipole or an oscillating magnetic dipole (or even electric/magnetic quadrupoles, octopoles etc.). Some reasonably sophisticated quantum mechanics tells us which of these possibilities is "allowed" or "forbidden" when an atom switches from one quantum state to another.

If during the switch the atom can behave like an oscillating electric dipole, then this is usually (for visible/IR/radio radiation at least) more efficient than the oscillating magnetic dipole or electric quadrupole etc. This would be termed an electric dipole transition. However, for certain changes of quantum state, the atom cannot behave like an oscillating electric dipole and the transition can only proceed (less efficiently - often called a "forbidden transition" in astrophysics) by the atom behaving like an oscillating magnetic dipole - i.e. a magnetic dipole transition.

Selvalakshmi,

At the risk of parrotting texts on particle physics, the electric dipole transition represents a coupling between a charged particle and the electric component of an electromagnetic field.

The magnetic dipole transition (I bet you can see what's coming next...) etc.etc.

By convention the hamiltonian of the interaction between a charged particle and an electromagnetic field is broken down into two parts - that resulting from the B field, and that from the E field: the magnetic and electric components respectively. Either transition may be permitted or disallowed depending on selection rules.

Needless to say, there are excellent wikipedia pages on both matters.

I'm not sure what level of answer you are looking for - the one above is fine, but here's a less sophisticated one.

Consider a dipole made up of a positive and negative charge separated by a small distance. If you make these charges swap positions, backward and forwards then you have an oscillating electric dipole that will generate electromagnetic waves.

Now consider a small conducting loop and pass a current through the loop that goes one way around and then the other. This is called an oscillating magnetic dipole and also produces electromagnetic waves.

In certain circumstances, an atom (or molecule or nucleus) can behave like an oscillating electric dipole or an oscillating magnetic dipole (or even electric/magnetic quadrupoles, octopoles etc.). Some reasonably sophisticated quantum mechanics tells us which of these possibilities is "allowed" or "forbidden" when an atom switches from one quantum state to another.

If during the switch the atom can behave like an oscillating electric dipole, then this is usually (for visible/IR/radio radiation at least) more efficient than the oscillating magnetic dipole or electric quadrupole etc. This would be termed an electric dipole transition. However, for certain changes of quantum state, the atom cannot behave like an oscillating electric dipole and the transition can only proceed (less efficiently - often called a "forbidden transition" in astrophysics) by the atom behaving like an oscillating magnetic dipole - i.e. a magnetic dipole transition.

Of course both are perpendicular to each other

Dimitrov and Jeffries are well explained everything. But it was asked a simple question: What is the difference between them?

    So, the simple answer.

Electric dipole is two electric charges.

The magnetic dipole is not exists.

   However, the field of currents, which are located in a limited area of space in the far distance from this area with a good degree of accuracy is described by the same formula. In this formula, the electric charges  are replaced by virtual magnetic charges.

Electric and magnetic dipole transition rates are first perturbation approximations. Perhaps this name is not very good because it can be confused with the idea of classical electric and magnetic dipoles. What is important to remark is that the electromagnetic radiation emitted or absorbed by an atom have transitions forbidden between certain atomic states which basically are obtained using Clebsch-Gordan coefficients in this first approach of the electromagnetic field. Let me to put the fundamental:

1. The transition rates are zero unless the difference between m initial and the m final is -1,0,+1.

2. In the same form the orbital momenta have to lf-li=-1,0,+1.

3. Finally, lf-li= odd integer

This means that , in the case of electric dipole transitions, the final and initial states must have different parities. For instance transitions like

1s to 2s

2p to 3p etc

are forbidden, while transitions

1s to 2p

2p to 3s etc

are allowed.

In contrast magnetic dipole transitions and quadrupole couple states with the same parity. A good book for seeing this topic is :

D.Griffiths, Introduction to Quantum Mechanics, Prentice-Hall,1995.

  Dipole is the first term of multipolar approximation (development in Taylor's series) which is applied to different physical issues. In electrostatic it is defiened as two electric charges separated by one distance d, while in magnetostic corresponds to a circle current with magnetic moment m. Physically they are the sources of the dielectricity and diamagnetism which provides an electric P polarization or M magnetization for certain materials. For instance, water has important P which is responsable to be less dense in solid phase than in liquid one.

  The same could be made with the propagation of the electromagnetic waves in guide or in a transmission line for the transversal electric TE and magnetic TM.

  But the question is:

What is meant by electric dipole and magnetic dipole transition?

Which introduce the transitions (between states). This concept of transitions does not apply classically and only is employed in quantum physics taking into account the Fermi gold rules.

  The name dipole, within this quantum  context, is sometimes hidden. The idea is the same that in classic physics: there is one Coulombic potential depending inversely of the distance 1/r, which is developed in multipolar form.  But now the Clebesch-Gordan coefficients apperas in function directly of the angular momenta, which have quantum rules for allowing photons to different states due to the conservation of the quantum numbers.

I hope that this can help.