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It usually means 'finding the main characteristics of a device'. This is often from a physical device you have made. So, you might create a transistor structure on silicon and then you need to 'characterise' it. You want to find out how it behaves under a variety of conditions, for example so you could model it.
So, for a transistor you might measure leakage, capacitances, charge storage, breakdown voltages, as well as the more obvious drain-source current versus gate voltage and drain/source voltage. Then, you actually know what you have made.