How can the energy released when bonds formed be harnessed to do work? I'm trying to understand how living organisms get energy from food. I've heard that "energy is released when bonds form", but what exactly does "released" mean?
If the energy dissipates in the form of heat, then how can the cell use it for things?
If the energy is not in the form of heat, what form does it take?
 A: In most reactions the energy is released as kinetic energy of the reaction products. If you consider some reaction:
$$ A + B \rightarrow C + D $$
then if you add up the kinetic energies of $A$ and $B$ before the reaction and add the kinetic energies of $C$ and $D$ after the reaction you'll find that the kinetic energy after the reaction is higher than before it.
Kinetic energy is basically heat, and while this is great if you're trying to run a steam turbine it's pretty useless if you're a cell. Fortunately there is a type of reaction called a redox reaction where the energy goes into exciting electrons. Redox reactions all involve pumping electrons around, and it's the energy of the electrons that cells can use to drive other reactions.
My knowledge of biochemistry is too sketchy to say much more, but one type of redox reaction you'll certainly be familiar with is the battery. Batteries use redox reactions to raise the energy of electrons, and that's how they power electrical circuits. Cells aren't like electrical circuits, but they use the energy of redox reactions in the same way to power the reactions they need to live.
A: The released energy does indeed take the form of heat, which is why fire is hot.
Cells use this energy to heat another molecule over the the threshold at which it will have an endothermic reaction, thus allowing them to force a reaction which would not normally occur at room temperature, or simply to heat the body, mantaining body heat even in an environment that is not as hot.
The reaction in particular that is used for this purpose is ATP -> ADP + P.
The produced ADP is then converted back into ATP while heated by the esothermic reaction C6H12O6 (sugar) + 6*O2 -> 6*CO2 + 6*H2O. This process is called cellular respiration.
