this diode carries the charging current through the relay into the battery. just DC where X marks the spot.
now the left half is just a boolean reference (is there mains power) and a power source to keep the relay open.
IMHO using a resistor to power a 3W led is, albeit cheap and functional, a cop out.
get a 3W led driver circuit on bidorbuy for R25, it will not only protect the led from transients but also the led wont dim when the battery voltage drops.