The higher concentrations of oxgyen help flush the nitrogen that has been absorbed out of the tissues. Percentage of deco gasses used varies by divers, agency and dive plans, but typically a deep dive will use 50% oxygen mix starting at their 70' stop and switch to 100% oxygen at 20'.
As you go deeper, the oxgyen toxicity becomes a concern. Deeper dives are more commonly being carried out on trimix, a mixture of helium, nitrogen and oxygen. The helium is used to displace some of the oxygen molecules, reducing the oxtox risk and to displace nitrogen, reducing the effects of narcosis.
The more oxygen you can add into a mix, the more you can speed up the offgassing of nitrogen from the tissues. However this has to be balanced against the risk of oxtox and is the reason for the use of multiple gasses.