How does Dalton's Law relate to scuba diving?
In scuba diving it is essential to consider the partial pressures of different gases for the following reasons:


The partial pressure of oxygen should be greather than 0.16 bar to avoid hypoxia (at the surface this partial pressure is obviously 0.21 bar).
Oxygen is toxic at high partial pressure. For the dive one want to stay as close as possible to 1.3-1.4 bar (maximum), while decompression is made with maximum 1.6 bar.
Nitrogen is narcotic at high partial pressure and we usually try not to go higher to partial pressure similar to what we have at 30-35m.


As an example consider a deep technical dive to 80m (9 bar). If you have air in your tank (21% oxygen, 79% nutrogen), the partial pressure of oxygen will be 
$$pp_{\ce{O2}} = p_\text{tot} \times x_{\ce{O2}} =  9\times0.21=1.89 &gt; 1.6,$$
thus you are in serious danger because of oxygen toxicity (visual changes, nausea, anxiety, irritability, confusion, dizziness, tonic-clonic seizure, ...) which can lead to death. If you want to have an optimal oxygen partial pressure of 1.4 you will need to reduce your oxygen content to 15% (less than air). But since the partial pressure of this new mixture at the surface is 0.15 &lt; 0.16 you should not start your dive with this tank.

In conclusion, what it is really important for your body is the partial pressure of the gas you are breathing, not the absolute pressure. Dalton's law is necessary to compute the different partial pressures.

This argument is quite advanced for scuba diving an you will have to search for technical diving in order to find the necessary informations. You may also want to look at other interesting physical phenomena that are important for scuba diving (Boyle's law, Charle's law, ...).