On-board DACs are pretty good these days. Unless you hear electronic noise / interference, a standalone sound card or external DAC probably won't make much of a difference. The one problem with on-board audio is often very high output impedance (I measured my laptop at 70Ω, and some Xonar models were measured at 100Ω!). It could (not necessarily) adversely affect the frequency response [*] and dampening factor of your headphones; another possible problem is insufficient power (not loud enough). The fix for both issues is a headphone amplifier with a low output impedance, ideally near 0Ω.
[*] The effect of an output impedance of just 22Ω on balanced armature IEMs whose impedance varies greatly with frequency (exagerated mids, no treble):
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Conversely, here's the effect of my laptop's output impedance of 70Ω on my 25Ω Denon AH-D2000:
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A slight 1 dB bump in the sub-bass region. Not much to write home about, so YMMV. My laptop doesn't get loud enough, though.
[*] The effect of an output impedance of just 22Ω on balanced armature IEMs whose impedance varies greatly with frequency (exagerated mids, no treble):
Conversely, here's the effect of my laptop's output impedance of 70Ω on my 25Ω Denon AH-D2000:
A slight 1 dB bump in the sub-bass region. Not much to write home about, so YMMV. My laptop doesn't get loud enough, though.