If you've taken Calculus classes, you should be aware of how sampling works and how accurate it can be. If you mow a fenced-in lawn (with a curved fence, much like a sine wave) with back and forth strokes only, and even if you get most of it, there's still some places you need to weed-eat. However, the smaller the mower, the more you accurately cut and the less weed-eating you need to do. This is analogous to sampling frequencies (samples of an analog audio signal).
If you look at a sine wave or simply, and audio signal, then draw exact non-overlapping
vertically-standing equal-width rectangles underneath the waveform, with no corners crossing the waveform line, (much like the mower swipes in a yard with a curved fence), you can see that the larger the rectangles, the more space under the analog waveform is not covered by the rectangles. All the rectangles are "measurements" to figure out the waveform in digital conversion (for illustration). The more slender width the rectangles are, the more you have to draw to take up the space, but you get a more accurate measurement of the analog signal.
This is analogous to sampling frequency. The higher the
sampling frequency, the more accurate the digital conversion. However, a poor clock can make some rectangles overlap or leave complete gaps.
Bit-depth (i.e. 16 or 24-bit) is a different measurement. It's more related to dynamics, and can apply more headroom from -infinity to 0db. I can't really get too technical here, but those two can be delved into and sold and bought separately. In other words, you can have 64-Bit 44.1Khz audio. Doesn't make sense to, but you can.
With that said, there are no A/D converters at 44.1Khz that are
really accurate. It's the analog electronics and clock in the unit that make for a better unit. If those are bad in a 192Khz sampling A/D converter, it can sound smeared and lacking detail. However, a 44.1Khz A/D with a tight clock and great analog electronics might sound terrific, but it may not accurately sample the higher frequencies (Like trying to mow a yard with a more severely wavy or zig-zaggy fence using a 30" wide mower that may just have to skip some of those crevices).