Also known as a sample and hold, this simple circuit will take an analog input and hold it high for as long as the RC time constant allows.
You can see with an AC waveform input the LED stays lit, with a constant voltage between 1.97V and 2V. This wouldnt ideally be used to light an LED from AC as there are other means to do so, the LED is just a load for example, this could be used for example as a debounce or to turn many signal inputs into one long input.