This is the cue for the pedant to chime in that it wasn't technically an explosion it was a deflagration (although technically I would still call it an explosion, but it wasn't a detonation). To be precise the destruction of the Shuttle Challenger proceeded through several very specific steps:

• Hot exhaust gases from the right Solid Rocket Booster (SRB) leaking through a failed joint between SRB segments impinges on the External Tank (ET) near the aft of the vehicle.
• These gases cause a burn through into the liquid Hydrogen tank and failure of the aft strut that attaches the SRB to the rocket stack.
• The right SRB pulls away from the aft strut, pivoting around its forward attachment point. At about this same time a small explosion at the bottom of the LH2 tank in the ET pushes it forward into the liquid oxygen (LOX) tank above it, disrupting both tanks.
• Both SRBs become detached and fly free as the ET falls apart, dumping its contents of liquid oxygen and hydrogen into the air where they then ignite in a deflagration explosion. There is a lot of energy in this fireball but this is not what destroys the Orbiter nor is it what kills the crew. This is a deflagration which is a very showy fireball but it is not a detonation with a powerful and destructive shockwave.
• As the Shuttle stack falls apart in mid-air the Orbiter is turned sideways into the supersonic airstream, the aerodynamic forces involved are extreme and they tear the vehicle into pieces. The crew cabin, however, remains largely intact.
• Very likely at this point all of the crew is still alive, and some are still conscious, but their fate is sealed. The crew cabin is just a box that is now flying a ballistic arc. Initially during the breakup the crew experiences well over 10 gees (possibly up to 20) of transient acceleration, which likely causes many of the crew to pass out. (Later, switches in the cabin would be found to have been activated by some of the crew who were still conscious after the breakup.) Finally, nearly 3 whole minutes after the vehicle broke apart the crew cabin smashes into the ocean at a quarter of the speed of sound, killing the entire crew instantly.

It is not known if any of the crew remained conscious throughout the freefall into the ocean. The cabin was damaged so severely by the impact that it could not be determined if it had lost pressurization before the impact, though some clues point to that being the case. During this period it was common for Shuttle crews to not wear full pressure suits during ascent. Their suits and non-pressurized air systems (PEAPs) were designed for egress on the ground only. After the Challenger disaster NASA moved back to using the Launch Entry Suits from the prototype flight phase of the program before switching to the more capable ACES suits used from 1994 onward. Which means that it was possible that if the cabin lost pressurization after breakup the crew could have been unconscious for most of the period preceding the cabin's impact with the ocean, but there's not enough data to know for certain if that is the case.

In any event, the wreckage from the crew cabin was similar to that of a jumbo jet hitting the water so the bodies of the crew were able to be recovered.

(Content warning: there are some slightly graphic descriptions ahead, so this is your opportunity to stop reading.)

When the cabin hit the ocean it was heavily damaged but remained largely intact. Finding the cabin was one of the top priorities of the recovery effort but it wasn't even located until more than a month after the accident, recovery of the crew cabin took weeks longer. None of the bodies of the crew were recovered fully intact due to the combination of the severe impact (with over 10x as much impact energy as a typical collision at highway speeds) and weeks of decomposition in the ocean. During the recovery the body of payload specialist Jarvis floated away and couldn't be located until over 10 days later. The identifiable portions of crew remains were given over to their relatives for burial or cremation, human remains that could not be identified (remember this is in an era before DNA testing was ubiquitous and easy) were collected and buried at Arlington National Cemetery within a special memorial for the Space Shuttle Challenger crew.