As somewhat of an audiophile, I cannot stand even a second of onboard sound.. although not all onboard sound is equal.. and its fine for rinky dink sattelite speakers, cheap ear buds, low end gaming headsets and such.. But I'm running studio monitors and there is no better way to get budget audiophile sound like from a mid-higher end sound card.
I've actually found realtek HD onboard sound to be the worst I've heard though. I had an older mobo with nvidia onboard sound that sounded far better.. I'd get a used Creative Audigy 2 ZS for $20-30 on ebay and you'd notice a somewhat significant increase in sound clarity over the Realtek.
You get a sound card to output ANALOG to high quality speakers or headphones, in order to take advantage what high quality DAC's you can find in PC sound cards.
I disagree with the post above.. the amp is only the third most important component.. The speakers are first, but the DAC is the easily the second biggest determinate of sound quality. (the digital analog converter .. but also the DSP, digital sound processor, is quite important) .. Any mid-higher end PC sound card (excluding the X-Fi chipset, which is garbage compared to real cards) is going to have a superior DAC to that of your receiver's, unless you have a $1,000 Marantz or something or start talking external DACs.
What types of headphones and/or speakers are you planning on using?