What is the difference between activity and reactivity when discussing elements?
Activity is an ordered series, showing which element will replace another element. For example, in a solution of copper sulfate in water, a piece of iron quickly becomes coated with copper as the iron displaces copper from the solution because iron is more active. No explosion took place.

$\ce{Fe(solid iron) + CuSO4 (dissolved in water) -&gt; Cu(solid copper) + FeSO4 (dissolved)}$

Reactivity is less clearly defined. In general, it means how easily some chemical change takes place. For example, chlorine, oxygen and sodium are all very reactive, easily attaching to other elements or replacing elements in compounds. Argon and helium are not reactive, and rarely, if ever, combine with other substances. Nitrogen triiodide, $\ce{NI3}$ and acetylene, $\ce{C2H2}$, are very reactive, but in a way opposite that of sodium or oxygen: rather than attaching to other substances, forming molecules, these compounds want to break up their molecules. In fact, even touching $\ce{NI3}$ will make it decompose violently... Now there's your explosion.