Vibration of atom confusion My book says:

When an atom absorbs heat energy, it starts vibrating from ground state.

What does this mean? What exactly is the meaning of absorption? How can an atom or an electron absorb energy? If it absorbs, where does it keep the energy and why does it cause the atom to vibrate?
 A: This sounds a bit like the Einstein model of a solid, where each atom is tied to a lattice position, vibrating independently around its equilibrium position without interaction with other atoms. The energy is the vibrational energy of a harmonic oscillator: kinetic energy + potential energy. It can acquire energy in some unspecified way (collisions with neighbors, conduction), but these interactions are not included in the Einstein model. This model explains the main features of heat capacity of solids.
In reality of course, there is no spring that ties an atom to an equilibrium position. The Debye model treats interacting atoms.
Besides by conduction, a solid can also be heated by radiation, especially be infrared radiation with frequencies in the same frequency range as dipole-active bonds.
A: 
How can an atom or an electron absorb energy?If it absorbs,where does it keep the energy?

Pieter has written an answer providing a summary of the absorption of heat. But I want to try and explain the part of your question above.
If we deal with electrons, they can either be a free state or what is called a bound state, that is they are likely to found in a region around the nucleus of the atom. I would like to say they are similar to little soccer balls in orbit around the nucleus, but that mental picture is misleading, so please just think of them as objects that are likely to be found near the nucleus. 
How close they get to the nucleus depends on the energy level they are most likely to occupy. The ground state is the lowest energy level and when an electron interacts with a photon, it can gain energy and be more likely to be found in the energy levels higher than the ground energy level. But the electron will almost immediately emit a photon of its own and return to a lower energy state. 
So the electron will not keep the energy, it will send it on in the form of a photon.
