So what's going to happen to the astronauts aboard the ISS - this was a resupply mission. How much longer can they stay up there with their current supplies?
They are stocked for months. As you can imagine, if your delivery mechanisms have a somewhat higher than usual risk of failure you don’t really go for just in time delivery.
There are several ways of supplying the ISS, though the very reliable Russian Progress (which also did have a failure recently – not a good year for cargo shipments to the ISS) is certainly the workhorse in terms of cargo shipments. (Though there is also the Japanese HTV and the – also recently failed – Cygnus.)
Any one or even couple failures of cargo vehicles in a row can’t do much to the supply situation. There are multiple redundancies built into the process. However, since really no one wants to abandon the ISS (just deserting it and coming back a couple months later is always risky with something as complex as the ISS that does require constant upkeep) that better be the case.
There will probably be quite some rescheduling and changing of plans happening. (I know that after the last cargo failure three people actually got to stay up in space a couple days longer, for whatever complicated scheduling related changes in plans.)
Not every space flight failure is the result of an explosion.
The Progress vehicle did actually enter an orbit (it reached space and was circling the Earth for a couple days), just the wrong one and after that it spun out of control and was no longer controllable from the ground. Since there is still some atmosphere and some drag in low Earth orbit it eventually was slowed down enough to burn up.
Basically, it failed because it couldn't be controlled anymore, no explosions involved. (Had it been launched to an higher orbit it may well have stayed up for a long, long time, no explosions or anything else interesting going on, just spinning round and round and being uncontrollable.)
