A displacement factor U is a tensor. The tensor elements Uij are the squares of the displacements u  (Δx, Δy, Δz in the directions a,b,c of the unit cell) of the electron density function from the coordinates in the crystal structure and at angles to these directions. In case of an isotropic factor, only the Eigenvalues (diagonal elements) have to be considered, in case of an anisotropic factor, all elements. The diagonal (isotropic) elements U11, U22 and U33 consider the displacements along cell edges and the other (anisotropic) elements the displacements  at angle to the cell edges.

I think this presentation here is helpful:

http://www.crystallographiccourseware.com/ThermalParameters/ThermalParameters.html

Thank you Rico...

They essentially tell you about the thermal motion of the atoms, so if the atoms are well defined you let them refime anisotropically and they look like American footballs as their thermal motion is not equivalent in all three directions. If you refine them isotropically then you contstrain the motion of the atom so it is the same in all three directions, so we do this for say H atoms or those atoms that misbehave or are not well defined. You have to be careful because all the error from your crystallographic measurment also goes into your displacement parameters and if you have incorrectly assigned an atom you will see very strangely behaved thermal parameters where sometimes they go non positive definate. You also have to treat them isotropically sometimes when you are dealing with disorder. The size of anisotropic displacememt parameters can often reflect disorder so say if you have a PF6 in your structure and you get really long elongated thermal elipsoids if you refine aniotropically because the electron denisty is being smeared over two positioms. Normally when we refine a crystal structure we put the atoms in isotropically first and then use the ANIS command in SHELX to refine them anisotropically. If you measure your crystal structure at low temperature then the thermal motion is reduced so your displacement parameters should be smaller and better behaved. So isotropic the displacement parameters look like Soccer balls and anisotropic they look more like American footballs. I hope this helps.

Also, if any of your thermal parameters refine to a negative value, it most probably means the absorption correction has not be done correctly. Anisotropic thermal parameters should be one of the last things you refine.

Thank you very much  Lawrence Margulies and Melanie Pilkington....All these information is will provide remarkable conclusion for my research...

I have a related question to your discussion

What does the number in parentheses of X-ray data mean?

Here for example: xyz coordinate for Ir-atom that is included in Ir-complex. The first question: what does  the bold number in the parentheses mean?

Ir1 Ir 0.18461(3) 0.28575(3) 0.160923(15) 0.04728(11) Uani 1 1 d . . .

The second question: I observed  similar parentheses beside bond length in some papers, for example Ir-C 2.179 (10), what does it mean also?