We are going to need to know the year, make and model to help you with that one.
bad fuse or relay switch
Check fuses. Do parking, tail, license plate lights work? same fuse could be rheostat to adjust dim to bright is broken
Check your wiring, but it is most likely the relay that selects bright or dim or a fuse.
check that both bulbs are the same and the connectors are on the same - if they are the same check ground connection
You probably have a bad ground on your "dim" light.
If you can see the oncoming vehicle then he can see you. Dim your lights at that time.
If you are a courteous driver, you will dim them when you see their tail lights. No one likes bright lights in their mirrors, reflecting into their eyes.
When driving at night with the headlights on, the radio and other display lights automatically dim. The bright button brightens those lights if you have trouble seeing them.
You need to replace the bulb in your lights. The dim lights and bright lights have different bulbs.
Its the dimmer switch bad.
A bad ground wire will cause dim headlights, or will cause lights not to work.
Chances are there is a short somewhere in the wiring