Blue stragglers are stars which stay on the main sequence (the normal, hydrogen-burning phase of a star's lifetime) longer than they are expected to.
The color of a star is a measure of its temperature and its mass - blue stars are hotter and more massive than red ones. The more massive a star is, the faster it burns up its hydrogen, so blue stars are expected to spend less time on the main sequence than red stars. Therefore, when you look at a color-magnitude diagram of a globular cluster (whose member stars all formed around the same time) you expect to see an orderly transition; stars which are bluer than a certain value (known as the "turnoff" point) will have already left the main sequence, while those which are redder will still be on it. The location of the turnoff point can be used to estimate the age of the cluster.
But, it is usually the case that several stars in a cluster are observed along the main sequence past the turnoff point, and these are referred to as blue stragglers. The most likely explanation for blue stragglers seems to be that they are the result of stellar collisions or mass transfer from another star. That way, a star which is red, cool and already somewhat old can get extra mass and turn bluer. It spent most of its life as a red star and therefore burnt its hydrogen at a slow enough rate to still be on the main sequence, but then at a certain point it gets extra mass and effectively "disguises" itself as a blue star, which makes us think it is younger than it really is.
This page updated on June 27, 2015