I just recently became Nitrox certified, so my explaination may be wrong.
But as far as I know, a nitrox compatible computer measures your ppO2, percent mix (i.e. 32% O2), along with some other factors.
The partial pressure is particularly important to monitor because as you go deeper you know that your ata increases. Well, with nitrox since there is a higher concentration of O2 you must be careful that the partial pressure does not exceed 1.4 (According to NAUI). If you exceed that partial pressure, you expose yourself to risks of oxygen toxicity which can lead to serve problems especially when you are relatively deep, lets say 80-100 fsw.
So having a computer that can accept a Nitrox mix will monitor your depth and ppO2 to ensure that you do not go too deep for your particular mixture of nitrox.
Hope this helps. If anyone who is more experienced in this realizes I have mistated please coorect me.
Rob