Ohm's law famously states V=IR, the voltage change (V) across a resistor generated by a current (I) equals the current multiplied by the resistance (R).
The resistor in this case is the cell membrane. When an experimenter injects a known amount of current through an electrode, the voltage change that occurs is related to that current by the resistance of the cell membrane. A high value indicates that the cell membrane does not let current pass easily so a given amount of current requires a large voltage changes.
The size of the cell and the number of open ion channels affect the input resistance. Larger size means lower resistance (more surface area for current to flow through) and more open ion channels means lower resistance (the conductance g=1/R increases when you open ion channels so the resistance decreases).
As for relevance to neural computation, higher input resistance means that less synaptic input (current injection) can lead to larger voltage changes. Manipulating input resistance (say by opening Cl- channels, which don't change the voltage of the cell much but do decrease the resistance) can change the responsiveness of the neuron to other inputs. This phenomenon is called shunting inhibition.