You see the number of revolutions that an electrical motor turns is dependent upon the cycles per second (Hertz) that the alternating current (AC) is changing. A motor that is designed to run on 60 Hz and is plugged into a 50 Hz power supply system will turn 17% slower, the internal current will go up 17%, the amount of power (watts) will go down 17%, and the appliance mechanical cooling will be 17% less. The end result will be that the motor will be using a higher current then what the motor was designed for, and this in turn will burn up the insulation of the electrical wiring which can result in burnout which could cause a fire because of the excessive heat.
An induction motor designed for 60 Hertz which is running from 50 Hertz power supply will draw more power and run hotter and slower. But this is unlikely to burn up the insulation and cause an outright fire unless the motor was designed poorly and running very hot on the proper frequency to begin with. Still, the consideration of smoke and fire is disturbing. The extra heat can be compensated for by using a fan or larger fan on the motor shaft to cool the motor.
Since output is proportional to torque and RPM the difference in output will be 1/6th less if a 60Hz equipment is changed to 50Hz. This occurs a lot with trailer mounted recap equipments. If the appliance has reduction gears (smaller frame gas turbines and aeroderivatives) then the gearing can be changed to keep the output from changing. Thus, larger frame gas turbines (i.e. no gearboxes) can't be swapped between countries with different frequencies, but equipment with reduction gears can be.
I've seen an entire plant relocated from 60Hz to 50Hz power system and some areas of the plant had significant problems due to the slower motor/pump speeds. Some equipment needed 50Hz to 60Hz converters to operate properly.
Aside from motors, in principle there is very little to choose between 50 Hz and 60 Hz. 50 Hz is slightly better for long distance power transmission because the power loss in the overhead lines is less. But a 50 Hz transformer needs about 17% more iron in it so it is are bigger and heavier.
When you use frequency converters for appliances, you'd better be careful in selection of the frequency converter.
Related article: Impact of 60Hz (50Hz) motor being used on 50Hz (60Hz) power supply