I have always found the Cornell to be a good source of info (and also the former home of Carl Sagan):
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.
I think the key takeaway is that we really aren't 100% sure. However, that in no way means that anyone can simply assert that their pet theory (guess, lie, whatever) is the answer either. Especially if they don't bring any evidence, testable hypotheses, or data to examine to the table.
Solstation also has quite a bit of good info on Blue Stragglers and what we know about them. Of particular interest is this graphic:
This paper from Cornell also has some additional info. Abstract:
In open star clusters, where all members formed at about the same time, blue straggler stars are typically observed to be brighter and bluer than hydrogen-burning main-sequence stars, and therefore should already have evolved into giant stars and stellar remnants. Correlations between blue straggler frequency and cluster binary star fraction, core mass and radial position suggest that mass transfer or mergers in binary stars dominates the production of blue stragglers in open clusters. Analytic models, detailed observations and sophisticated N-body simulations, however, argue in favour of stellar collisions. Here we report that the blue stragglers in long-period binaries in the old (7 × 109-year) open cluster NGC 188 have companions with masses of about half a solar mass, with a surprisingly narrow mass distribution. This conclusively rules out a collisional origin, as the collision hypothesis predicts a companion mass distribution with significantly higher masses. Mergers in hierarchical triple stars are marginally permitted by the data, but the observations do not favour this hypothesis. The data are highly consistent with a mass transfer origin for the long-period blue straggler binaries in NGC 188, in which the companions would be white dwarfs of about half a solar mass.