I use digital connections because I like the convenience of a single cable, and because I'm using computers like Mac Minis now - that do a nice job with optical digital audio or HDMI but don't have the greatest analog audio output (much like your motherboard). That might be due to the DAC in the Mini, or just a poor headphone amp.
To try and break it down - the music on your computer is digital, and your speakers need an analog signal to play - so the amp needs an analog signal to amplify and send to the speakers. Therefore, somewhere along the line, something needs to convert your digital music into an analog signal. You can have your computer do that, an external sound card do it, an external DAC do it, or a DAC built into the amp do it. (Yeah, I probably missed some options.
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Some folks care about DACs down to the nth degree...I'm not one of them. I think that my Pioneer Elite receiver sounds great, and it is using its own DACs. I plug headphones into my phone and think it sounds great, and the phone is using its DAC. I think that there was a bigger difference between DACs 20 years ago, but they are so common these days that a lot of them are good. Your motherboard audio might not be great for some other reason besides the DAC (such as a junky amp on the output).
You could try a really inexpensive external dongle like
this one just to check if the audio improves on your Onkyo. I'm not convinced that a <$10 dongle is going to be better than your motherboard, but it might be.