Biomolecular stability refers to the ability of a biomolecule to withstand external stress, i.e., to keep its designated structure and activity. Most often increasing temperature is used to determine stability, but other stresses could be used too, such as pH or agitation. The relevant stability is determined by the stress-induced loss in a structure that already gives rise to a loss of function, too. This could be due to a structural change around the active site of that protein. In addition to that, proteins often have intermediate states that still conserve some part of their native structures and with some residual stability. The figure below shows these different states as an example of a thermally stressed protein (apoflavodoxin).
Figure adapted from: Lamazares, E., Clemente, I., Bueno, M. et al. Rational stabilization of complex proteins: a divide and combine approach. Sci Rep 5, 9129 (2015))