A horizontal monopoly is a situation in which a single company owns or controls an entire stage in the supply process.
For example, if one company controlled all paper manufacturing they would be said to have a horizontal monopoly in paper manufacture. This would then allow them to leverage on this monopoly, and inflate the price of paper to ridiculous amounts. With paper being so essential in today's world (we havent quite achieved the paperless office yet.) consumers would have no alternative but to pay whatever extortionate prices this firm decided to charge.
Of course, inflating the price too much will make it feasible for other companies to start supplying paper at lower cost, whilst making a profit. As paper production is a relatively simple process, it would then become highly unlikely that this theoretical monopoly would last long.
Contrast with: Vertical Monopoly.