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Bond Strength
By definition, the higher the bond dissociation energy, the stronger the bond. A weak bond takes much less energy to break than a strong one. The average bond dissociation energy for a carbon-iodine bond, for example, is 51 kilocalories per mole, while the average bond dissociation energy for a carbon-fluorine bond is 116 kcal per mole, which implies that carbon-fluorine bonds are much stronger than carbon-iodine bonds. Likewise, double bonds are much stronger than single bonds (although many reactions involve breaking only one of the two double bonds rather than both of them).
Caveats
It's extremely important to realize, however, that these figures and others like them are only averages. That's because the strength of a bond varies depending on what else is positioned nearby in the molecule. You may have heard, for example, that phenols are much more acidic than alcohols, which implies the O-H bond in a phenol is easier to break than the O-H bond in an alcohol. Consequently, you should always bear in mind that average bond dissociation energies are only averages and treat them as such.
Reactivity
Ultimately, the strength of each bond determines how easy it is to break and whether a reaction involving that bond will be exothermic (heat-releasing) or endothermic (heat-absorbing). If the bonds formed in a reaction are stronger (have higher bond dissociation energies) than the bonds that were broken, the reaction is exothermic, and the product is more stable or lower in energy than the reactants. If a reaction exchanged an iodine attached to a carbon for a fluorine attached to a carbon without making any other changes, for example, you can predict that the reaction would be exothermic, because the bond that was broken was weaker than the bond that was formed.
Reactions
If you add up the bond dissociation energy for all the bonds that break in a reaction and subtract the bond dissociation energy for all the bonds that are formed, you can often get a rough estimate of the amount of heat energy released (or absorbed) by the reaction. If you are looking at hydrogenation of 1-butene, for example, you would need to break a C-C π bond, break an H-H bond and form two C-H bonds. The average bond dissociation energies are 63 kcal / mole, 104 kcal / mole and 99 kcal/mole, respectively, so 63 + 104 - 2 x 99 = -31 kcal / mole, which means this reaction is exothermic. As it happens, the measured heat of hydrogenation for 1-butene is -30.3 kcal / mole, so in this case the figure you get from the average bond dissociation energies is actually a pretty good estimate.