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No op-amp is perfect. All op-amps differ from the ideal op-amp described above. You don't usually need to be concerned about these parameters because you don't usually need that kind of precision. However, if you need precision, you need to know these parameters and how to compensate for them.
The output voltage of an op-amp should be 0 volts if the inputs are exactly equal. However, real-world op-amps have a small output voltage when the inputs are equal. The input offset voltage is the input voltage difference required to make the output zero volts. This is often compensated with a voltage divider on one input or a bridge circuit on the inputs.
Assuming a configuration with a gain of 1 (such as an inverting amplifier with equal resistors or differential amplifier with equal resistors) the output voltage should be the exact difference between the two input voltages. In real-world op-amps, there will be a slight output voltage when both inputs are exactly equal and the output will not be the exact difference between the two input voltages. If the configuration has a gain greater than 1, the output voltage differs from the difference between the input voltages even more. The common-mode rejection tells how close the output voltage is to the exact difference between the input voltages. This is often compensated by a specific series resistor on one of the inputs.
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