A marquis is a nobleman. If you're a marquis, your rank is higher than a baron or a count, but lower than a duke or a prince.
In systems like monarchies, where people inherit a certain rank, a marquis is one of the title given to men. The French spelling, marquis, is common in most parts of Europe, although in Britain they prefer marquess. Sometimes being a marquis includes some real power to rule a territory, but it's more often just an honorary title. The equivalent for a woman is being a marchioness.