A loss factor can refer to a multitude of things in dynamics. Most often, it refers to the conversion of vibration energy into heat. This process is (nearly) irreversible, which is why the energy is thought of as 'lost', hence, the phrase a damping loss factor.
You find a discussion on the topic of damping here
Loss factor or specific damping factor is defined as the energy dissipated per radian to the peak potential energy is the cycle. This is a very useful method to compare the damping capacity of different materials. It has to be pointed out that this method is used for materials with very light damping. For more information, please have a look at the book "Dynamic of Structure", written by Anil K Chopra.
Is loss Factor a property of the material ? - ResearchGate. Available from: https://www.researchgate.net/post/Is_loss_Factor_a_property_of_the_material#56e4b824ed99e1961120368f [accessed Mar 13, 2016].
Loss factor is a material characteristic (usually know as Tangent of delta for those working with polymers and often defined by \eta symbol).
Modal damping is a characteristic of the response of a damped dynamic system when represented by a modal model (eigenvalues/natural frequencies vector, eigenvectors/mode shapes matrix, and modal damping vector).
If the materials of the dynamic system have a large loss factor, then the modal damping vector representing the response of the system will have larger values and the frequency response model will present a large damping effect.