A large, high-voltage electrolytic capacitor (usually rated at 400V or 450V, between 47µF and 120µF). It smooths the pulsating DC into a stable high-voltage DC rail (roughly 310V to 340V depending on local mains voltage).
Limits inrush current when the device is first turned on.
If you are looking for the schematic to fix a "dead" unit, start with these common failure points:
Dried-out filter capacitors on the secondary rails fail to smooth out ripple current, resulting in voltage drops under load. Tips for Finding Free Schematics Online
. Look for "bulging" or leaking caps, especially on the secondary output side. Backlight Fails (2-Second to Black)