Yes, bead not correctly seated on the rim.
On pretty much every clincher tyre there’s a band a constant width around the inside of the tyre just by the bead (the wire or kevlar bit that doesn’t stretch and keeps your tyre the same circumference). That band should be visible all the way round the tyre when it’s mounted properly on the rim.
The best way to ensure this, when fitting a tyre, is to pump it up to about 10-15psi and examine the bit between the rim and the tyre – that band should be a constant width. If it’s all wobbly and going up and down as you rotate the wheel, the bead is not properly “clinched” by the hooky bit of the rim.
Sometimes it’s not a problem and people ride on wonky tyres for years. Sometimes as you inflate the tyre, the air pressure forces the bead away from the rim if it’s not seated properly. In spectacular cases, this pushes the bead out and a bubble of inner tube rapidly forces itself between bead and rim, which then explodes with an impressive BANG, shreds the inner tube and sometimes briefly deafens the hapless mechanic inflating the tyre.
I’ve seen it happen a lot of times. It’s most likely when you haven’t checked the tyre properly at low pressure, and it’s easiest to do if you’re inflating from an airline (compressor), especially to high pressures. It’s actually quite impressive to behold but I wouldn’t recommend being very close to it when it happens.
Some tyres are an absolute b*tch to seat properly. The old Specialized Armadillos, and current Schwalbe Marathon Plus (and actually quite a lot of Continentals) were tight and could be a real hassle to fit well. Patience and a bit of tyre-pulling brute force are key.
: P