AvonKerr and Surprised Seagull gave great answers.
But in case people are curious about specifics, an NIJ rated bomb suit has to withstand the detonation of 1.25 lbs (~567 grams) of C4 at a distance of 2 feet (~0.6 m). For reference, the Claymore mine has 680 grams of HE filler, which is around 20% more than the test charge.
In addition, the intensity of an explosion pressure wave declines with the cubed root of the distance from the explosion. So someone standing 2 feet away experiences around 9x less blast pressure than if the explosive were strapped to them, which would definitely kill the person.