Is it the current you have to drive in the input to get a specific, defined voltage at the output? And don't the currents cancel each other when applied to both inputs?
The ideal opamp has infinite input impedance. That means its inputs don't draw any current at all. There is no such thing as a ideal opamp, so all opamps draw some amount of current. This is what the input bias current spec tells you.
Any current times the impedance of whatever is driving the opamp input will cause a voltage, which is a error voltage between the real signal and what the opamp sees. This error is added directly to the input offset error of the opamp to get the effective offset error for your circuit.
For example, if the opamp input bias current spec is 1nA, then must assume a voltage error of 1mV with a 1MOhm resistor in series with that input. This is in addition to other sources of error, like the input offset voltage spec.
Different opamp technologies can vary widely. Old bipolar input opamps like the LM324 have orders of magnitude higher bias current than FET input opamps. For something like a LM324 you have to consider the input bias current spec carefully. For many modern CMOS input opamps the input bias current is so low that you can often ignore it (after a quick calculation to verify this for your case of course).
The input bias current spec is for each input. These do not necessarily cancel since the polarity can not be guaranteed. Some opamps have a input offset current spec that tells you the worst case current mismatch between the two inputs. That is common in bipolar input opamps since the current direction and magnitude is somewhat known. For example, the LM324 is specified for 100nA input bias current, but only 30nA input offset current. CMOS input opamps often don't have a offset current spec since the bias current is due to leakage and there is go guarantee what its polarity is.