I have a circuit that worked fine on a a 12v lead acid battery for a day. Once connected to a 12v 3a power supply it didn't work properly and then the ams1117 5v burned up and so did a 3.3v one within a few minutes. The 12v power supply is a cheap Chinese model from eBay. My meter shows 12.3v but I don't have a scope. I understand that ripples in the output of the power supply have probably caused this but what does that mean and how has it exceeded the rating of the converter? Is there a simple fix so I can use the power supply? Would a 12v motor or relay be susceptible to the ripples? I'm going to run my esp8266 from a different source but I'd like to keep using the power supply for the motor and 12v relays.
Running an Arduino board with 12V is almost always too much. With only a few leds the voltage regulator on the Arduino boards gets too hot.
The best voltage is 7.5V. Then the voltage regulator has only little power dissipation and it is just high enough to turn off the USB 5V power.
Or power the Arduino board with a 5V (from a USB charger, or USB power pack) to the USB connector.
Never use a power supply that is not certified. It is a safety risk that can be avoided with a few dollars more.
The cheap power supply can have ripples, but it can for example have noise in the MHz range, or a voltage spike when turned on, or voltage overshoot when more current is required. There can also be a coupling to the mains as @Majenko wrote. I have had a few of those. Nasty stuff!
Even with a scope, you can not tell if the power supply is really okay.
If you have a unreliable power source or a voltage that is too high, then a DC-DC converter can convert it into a nice steady voltage.
However, you should first get rid of that cheap power supply and buy a good one.