What exactly is a reducing equivalent and what does it do?
The number of "equivalents" of a reagent refers to how much of the reagent there is relative to another reactant of interest. To use a concrete example, if we are interested in the $\mathrm{S_N2}$ transformation $$\ce{CH3Cl -&gt; CH3Br},$$ a possible way of bringing this about would be to treat the starting material (methyl chloride) with a certain amount of bromide ion. If we carry out the reaction on 0.5 mol of methyl chloride, in theory we would only need 0.5 mol of bromide ion, because of the stoichiometry of the reaction:

$$\ce{CH3Cl + Br- -&gt; CH3Br + Cl-}$$

In this case, 0.5 mol of bromide ion would be referred to as being "1 equivalent" of bromide (relative to methyl chloride, which is the reactant of interest).

We could also say that for the complete combustion of hexane, we would (theoretically) need "9.5 equivalents" of oxygen gas:

$$\ce{2C6H14 + 19O2 -&gt;12CO2 + 14H2O}$$

In the case of a redox half-reaction, you usually have electrons in either the reactants or the products:

$$\ce{Fe^3+ + e- -&gt; Fe^2+}$$

(this highly simplified reaction is relevant in, e.g., cytochrome c's role as an electron carrier in oxidative phosphorylation). Under biological conditions, this is rather unrealistic, as electrons don't actually exist in aqueous solution, nor is there any electrolysis going on. So, you need something else to act as a supplier of electrons, i.e. a reducing agent, such as NADH.

$$\ce{NADH + H+ -&gt; NAD+ + 2H+ + 2e-}$$

In this case, because 1 mol of NADH provides 2 mol of "electrons", you could say that NADH acts as two reducing equivalents. Here, NADH is acting as a reducing agent, and is itself oxidised to NAD. [I don't agree with the Wikipedia page about hydride ion being one reducing equivalent; it should be two.]