What would happen if a gamma ray burst exploded near the sun?

It is hard to imagine what would happen, and it would depend on how close the burst was.

Some astronomers have speculated that over the last 500 million years the sun has been close to several of these bursts, and that the ensuing damage to the earth caused some of the great extinctions that we know about from the fossil record.

Gamma ray bursts, however, seem to be a feature of a YOUNG universe because they have only been detected at 'cosmological' distances presumably in excess of several billion light years. That means that true GRBs were only common when the Milky Way was billions of years younger than it is now.

It is also true that gamma-ray bursts are associated with the most massive stars in the universe in excess of about 20 times the mass of the sun. The star forming region Eta Carina only 4000 light years away hosts several stars with masses of 100 times the sun, and these will definitely be potential gamma-ray burst progenitors in the next few million years. Luckily, the axis of the most massive of these stars is tilted away from our line-of-sight, so its gamma-ray jet will not pass this way.

We may be comfortably past the epoch of gamma ray bursts in the history of our galaxy...however the soft-gamma repeaters are related to supernova remnants and may have another origin than classical GRBs. In which case, our susceptibility to these would be about the same as the sun being near a supernova explosion during the remainder of its lifetime.

The prediction is that the ozone layer would instantly vanish and we would probably be affected by the influx of cosmic ray particles to the extent that genetic damage is likely...perhaps even leading to extinctions of some life forms.