The diver will consume her breathing gas at a faster rate, because each lungful of breathing gas is at greater pressure. A diver at 60 feet will breathe roughly 3 times as much gas as a diver at the surface. A diver at 130 feet will breathe roughly 5 times as much gas.
The diver will start to suffer narcosis at deeper depths. For divers breathing air (the most common breathing gas) or nitrox, narcosis usually starts to become noticeable at about 100 feet. Divers breathing helium mixes can get much deeper. Narcosis slows the mental and physical reactions of the diver.
The diver's body will absorb gases from her breathing mixture at a faster rate. If the diver stays deep enough and long enough, she will have to perform decompression stops before ascending to the surface, or risk injury (or even potentially death) from decompression sickness. Divers normally use tables or dive computers to stay within no-decompression limits.
At deeper depths, more spectrums of visible light are absorbed by the water. Accordingly the deeper you go, the more everything will start to look blue and green. The total light is also reduced, and so in low visibilty conditions, torches may be need once the diver descends to a certain depth.
At deeper depths the water is colder and so the diver will also get colder, faster.
Because the breathing gas is more dense at depth, breathing resistance will normally increase. Divers intending to dive deep usually use high performance regulators and/or helium mixes (which is a less dense gas) to reduce the effects of this. Divers have to be very careful not to exert themselves at depth (which breathing resistance can contribute too), as they can suffer from increased CO2 retention which can lead to hypercapnia.
If the diver is diving an oxygen rich mixture, such as nitrox, the diver can be at risk for oxygen toxicity. Divers using nitrox are trained how to avoid this. It is theoretically possible, although highly unlikely, that a diver breathing air could suffer oxygen toxicity if they went deep enough.