Williamson synthesis is basically a S_N2 reaction of a primary alkyl halide with an alkoxide ion. The basic mechanism for this reaction is

Now consider this reaction,

This reaction proceeds as conventional Williamson synthesis. But if secondary or tertiary alkyl halides are taken in place of primary alkyl halides, then elimination would compete over substitution reaction, which will result in the formation of alkenes. The reason is alkoxides are better nucleophiles as well as strong bases. Therefore, they react with alkyl halides resulting in an elimination reaction.