1) One LED part number has a range of forward voltages. If you use a simple resistor then some LEDs will have a higher current (and higher brightness) than others. The ones with the higher current might burn out.
2) The power supply might not be regulated and have a voltage that is too high sometimes. Then the current will also be too high sometimes if a simple resistor is used then the LEDs burn out.
3) A battery might be used instead of a power supply. If a simple resistor is used then the LEDs will get dimmer and dimmer as the battery voltage runs down.
A current regulator solves these problems.