As Zacsmaster says, it is the gaps or interstices between the rock grains that contain the oil in an oil reservoir.
Think of a big box of marbles and then filled with water - if you removed the water, the volume of marbles will not decrease, as the water is not in the marbles themselves, but the gaps around them. The marbles continue to rest against eachother and support the whole.
Put simply, when an oil reservoir is tapped, the overlying pressure of rock forces oil out of the reservoir, emerging at the well head - this is known as Primar Recovery. As more oil is extracted, the pressure decreases, and some of the hydrocarbons change to a gasous phase, replacing the liquid oil in the interstices. Once the reservoir pressure drops too low, no more oil rises out. However, the reservoir is by no means exhausted. Probably only 20-25% of the crude oil contained in it has been recovered.
This is where oil companies use Enhanced Oil Recovery (EOR) techniques to extract more oil. This can invlove pumping steam, gases, seawater, or mixtures of seawater and chemicals. These are intended to re-pressurise the reservoir or to reduce the viscosity (thickness / stickiness) of the oil, so that more can be extracted.
This can occur in stages, for example, after Primary recovery is finished, the Secondary phase will pump, say, natural gas (collected at the well head) back into the reservoir to re-pressurise and extract more oil. When this again declines, additional gases will be added which help to reduce the oil's viscosity and to 'thin it out' which helps to recover even more.
Early methods of enhanced recovery usually involved pumping seawater into the reservoir, but this, in certain cases, has the tendency to ruin it for any further exploitation. So, as methods have advanced, previous reservoirs remain irrecoverable due to the ruinous effect the earlier methods had.