Dehydration happens when there is a loss of fluid from the body. Even in a moderate hour long training session, you might lose up to 1 litre of sweat, more if exercising for longer or in hot temperatures. If you’re dehydrated and exercise, the risk of you developing heat illness greatly increases, as your body can’t sweat as much to cool you down. Heat illness is very serious, and includes things like heat cramps (involuntary muscle spasms), heat exhaustion (weak pulse, lower blood pressure, headaches) and heat stroke (most serious and needs a doctor straightaway, can potentially kill you as your internal systems fail).
As Laura Anne has mentioned doing exercise whilst dehydrated can be dangerous, though this will depend on the extent of the dehydration (i.e. amount of body mass loss) and the exercise you are doing (i.e. intensity and environmental conditions). Most elite runners at the end of an endurance race will be dehydrated. During the race athletes do not consume exactly the same amount of fluid lost through the evaporation of sweat. As they in pursuit of the quickest time, drinking so much fluid would disrupt their race. The issue comes when people are not replacing fluids after racing etc. or not consuming enough during the race becoming severely dehydrated. The result of this is very serious leading to heat related illnesses and can be potentially fatal.