Understanding MOSFET characteristics
These parameters are related to each other and are important because they determine how hot the MOSFET gets during operation.  Excessive junction temperature will destroy the device quickly. It is important to note that these parameters are specified under a certain set of conditions, such as junction temperature, gate voltage, drain current. Datasheets have graphs describing how the parameters change as these conditions change.
A MOSFET is not an ideal switch; it has a small amount of resistance when it is on.  This is the drain-source resistance parameter.  Note that this is normally spec'd at 25 deg C junction temperature; its value can double at max temperatures.
The drain current is the maximum continuous current the device can conduct.  Note that this value is usually spec'd at 25 deg C case temperature, which is normally hard to maintain.  It should be regarded more as a figure of merit rather than a realistic maximum current for the device.
The drain current flowing through the drain-source resistance causes a power loss in the device, which is manifested by heating at the junction.  This heat has to dissipate into the environment; heat flow is limited by the thermal resistance of the package, which is spec'd on the data sheet.  The maximum power dissipation is the maximum amount of power that the package can dissipate without exceeding the maximum junction temperature.  Again, this value for the condition that the case is maintained at a certain temperature.  As in the case of the drain current, this figure is only a starting point.
So, how do you know if the chosen MOSFET is suitable, from a heating point of view? Most MOSFETS have a max junction temperature of 175 deg C, but you really don't want to be operating that high.  100 to 125 deg max is more reasonable.  So, take your device, look up its drain-source resistance at 100 degrees.  You know what the current is, so calculate the power dissipation: power = amps squared times resistance.  Multiply this power by the thermal resistance, add this temperature rise to the ambient temperature, and see how close the junction temperature is to 100 degrees.  If it's under 100, then you're good.  If it's way under, you could maybe choose a smaller MOSFET.  But if it's over by more than a little, you should choose a device having lower resistance, or in a package having a lower thermal resistance.