
I get to do some of this in my research with colleagues here at Penn State and elsewhere. Coal is a wonderful material! While it looks solid, if you select the appropriate rank of coal, the structure is full of very tiny holes, so small they are too small to be holes–so we call them pores. The very small pores are known as micropores and "here is where the magic happens" (for you celebrity crib fans). There are larger pores, and also very large pores or cracks in the coal, which are very useful for increasing the permeability (speed of access of the gasses into the coal).

In the gas phase (there are three phases: solid, liquid, and gas for most things) the molecules or CO2 are bouncing around. We can increase the pressure (more gas molecules in the same volume as before) but that takes work. The molecules like their space and anyway we are decreasing their entropy. But if we put a molecule of CO2 into a coal micropore there is an attraction between the matrix and the CO2 molecule. Now the CO2 does not need as much space, it wants to associate with the coal and thus we can put in more CO2 into coal than we could into the same volume of empty space (bloody marvelous!).
There are a couple of other advantages too. Remember that methane is often in these pores too (if we are at the bituminous rank range), well, CO2 acts like an invading army and kicks out the methane (it competitively replaces the methane molecules). Thus, you could sequester CO2 into a deep coal seam, collect the methane that is released from the coal (coal bed methane), combust that and put the CO2 formed back into the coal seam. Thus forming a closed loop of emission free (CO2 anyway) electricity for as long as the methane lasts. As we have lots of coal, much of it is close to large point sources of CO2 (such as a power plant), then this all makes sense.

There are only a couple of minor details, the main one being cost. If the pumping and separation of the CO2 costs $ then the price of the electricity generated will increase. We are not yet in a competitive region for any of the sequestration technologies (maybe enhanced oil recovery). Selling methane certainly helps to lower the cost of sequestering CO2 into coal but the cost is still too high. There are a couple of locations where we are currently pumping CO2 into coal.
Details here if you would like to know more.