Another way to think about bond "strength" is how much energy is needed to break a bond apart (or how much energy is released when a bond forms).
These "bond energies" can be experimentally determined for simple molecules and estimated for others.
They can also be roughly compared with electronegativity differences. For example, the change in bond energy for the molecules HF, HCl, HBr and HI is based on the decreasing electronegativity of the halogens as you move down the column.
WHY WE CARE: the changes in bond energy during a reaction are responsible for the heat energy associated with a chemical process. In simplest terms this overall heat can be thought of as the bottom line of a balance sheet comparing the energy used to break old bonds and the energy released when new bonds form.