A sedge is a grass-like plant (graminoid) in the sedge family (Cyperacea). Most would look down the sedges while walking through the woods or a wetland and just think they are grasses. While they fill much the same ecological role as the true grasses (Poaceae/Gramiae) they are botanically unique.
One thing that most people learn about sedges is the saying “sedges have edges” This refers to the triangular-shaped cross-section of many sedge species. If you roll the base of the majority of the sedge species, particularly the Carex and Cyperaceae, between your fingers, you feel the edges plainly. If you were to cut the stem in cross-section, you would notice the triangular shape.
There are many exceptions to the rule. Most importantly there are other plants like Common Bur reed, and Sweet Flag have triangular stems that are not in the sedge family. Then there are those species like softstem bulrush that have perfectly round stems. Beware the “sedges have edges saying”, it is a good start, but not a 100% rule.
The flowers and seed of sedges differ from the grasses, and I would refer you to any good botany book for more information and detailed drawings. For wetland plants of the Midwest I would recommend A Great Lakes Wetland Flora. http://www.amazon.com/Great-Lakes-Wetland-Flora-complete/dp/1478194693