What is burden of current transformer?

The burden on a CT is the sum total impedance connected to the secondary - including the CT secondary winding coil resistance, lead resistance, and any loads attached (relays, meters, etc.).

If this is for power calculations and CT saturation in three phase systems, remember you must multiply the lead resistance by two to get the total path resistance.
Another Answer

We use the word, 'burden', to describe the load supplied by the instrument transformer's secondary. This is normally a measuring instrument or protection relay. We use the word 'burden' to distinguish it from the 'load' supplied by the circuit to which the primary winding is connected.