This is a Very Simple AC LED Driver Circuit for driving a 1 watt LED on 110, which may be understood with the following points.
The .47uf/400V capacitor at the input forms the heart of the circuit and functions as the main current limiter component of the circuit. You can use 1uf/400V capacitor for better performance.
However high voltage capacitors have one serious issue, these do not restrict or are not able to inhibit the initial switch ON mains power in rush, which can be fatal for any electronic circuit LEDs are no exceptions.
Adding a 10-56 Ohm resistor at the input helps to introduce some damage control measures, but still it alone cannot do the complete safeguarding of the involved electronics.