Loosely speaking, the audio signal path in the sound card looks like this:
Microphone -> Preamp -> | Vol.Cntrl -> PowerAmp -> Speaker
D/A Conv-> |
LINE-IN -> |
|
V
LineOut
So basically, The LineOut is a signal output (high impedance, low power capability) intended for an external amplifier or powered speaker. It may burn out if you overload it.
The speaker output is a power output (well cooled power elements in circuit path) with low impedance, to connect to a passive speaker; You can't damage it by connecting a powered speaker (because you will be drawing less power than this output is designed for) but the sound quality will be lower because you will be picking up all the distortion from the power amplifier.
Most probably, the headphone output is a "convenience outlet" on the front panel (so that if you plug in a headphone, the speakers are cut off). In audio quality devices, it may have a separate headphone power amplifier, with lower noise/distortion, lower peak volume and lower peak power capabilities. If so, plugging in a passive speaker into this jack may damage the headphone amplifier (because it may not be able to dissipate all the heat generated by the extra loading), or just give you lower peak volumes.