Voltage
The discussion above only talks about charging current (amperage), but there’s another factor worth considering, and that’s the voltage of the charger. This is what’s most likely to get you in trouble, since if you were to connect, say a ten-volt charger into your iPhone (which expects five volts), that would almost certainly damage your iPhone — possibly irreparably. It still wouldn’t overcharge the battery or cause an explosion, although it would almost certainly burn out the charging circuits between the Lightning port and the battery. You might even see smoke or smell burning if you tried such a thing.
That being said, in over two decades of working with USB power adapters, I have never encountered one that doesn’t provide five volts. A company would have to be completely out of touch with reality to release a USB charger that far out of the USB spec, which requires that everything USB be five volts and only five volts.
What you’re more likely to encounter in a cheap USB charger is poor voltage regulation. This means that it may not provide a “steady” five volts, but could shift around between, say, 4.5V and 5.5V. This will not cause noticeable damage to your iPhone — most electronic devices are designed to handle this kind of variance — but it may affect your charging efficiency, and could even shorten the life of your battery compared to using a proper charger that stays within proper tolerances.