What is Zaitsev's rule ?

Zaitsev's rule (or Saytzeff's rule, Saytzev's rule) is an empirical rule for predicting the favored alkene product(s) in elimination reactions.

Zaitsev's rule states that: "The alkene formed in greatest amount is the one that corresponds to removal of the hydrogen from the alpha-carbon which is attached to the fewest hydrogen atoms."

For example, when 2-chlorobutane is treated with alcoholic potassium hydroxide (KOH).  The major product is 2-butene as hydrogen atom is removed from C₃ which is attached to 3 hydrogen atoms, while the minor product is 1-butene as hydrogen atom is removed from C₁ which is attached to 2 hydrogen atoms.

CH₃CH₂CHBrCH₃ + alc. KOH → CH₃CH=CHCH₃ + CH₃CH₂CH=CH₂
                                                     major product       minor product
                                                       (cis + trans)

When doing an elimination reaction on an alkyl halide, an alkene is formed. Alkenes are most stable when they are on carbons that are attached to more carbons, as opposed to hydrogens. Zaitsev was a Russian scientist who studied the products of elimination reactions and empirically observed that doing elimination reactions results in the formation of alkenes with pi bonds on the most substituted carbons possible. We now know that this is due to the thermodynamics of making the most stable product. This rule; however, does not apply to sterically hindered bases (such as potassium tert-butoxide), wherein, a less substituted product (called the Hoffmann product sometimes) is formed, as the steric hinderance increases the energy of the transition state of the Zaitsev product.

Tl;dr: When doing an elimination reaction, the most alkyl substituted alkene product possible is the major product when using bases without too much steric hinderance.