One of the wires is probably broken. Probably can't be fixed.
ahh, it can though, i have done it multiple times. if its a wire, it can be fixed, if its the speaker itself, then you will need to purchase new earbuds, unless of course, you happen to have a spare earbud that you could solder on.
you will need to find a spot that is subject to excessive flexing and/or has exposed wire showing, as this would be the most likely place where a wire break could occur. the most usual places for the wires to break, due to excessive flexing, would be at the point of entry in the earbuds themselves or the point of entry in the audio jack. you can purchase new jacks if the break in the wire is too close to the jack.
if you do plan on soldering, just take note that the wire is covered in a thin layer of laquer. before soldering the wire you will need to sand off the laquer insulation to expose the bare copper.