Current, in an electronic circuit, is the flow of the charged particles (electrons). The current is measured by the number of charged particles passing the point of the circuit, that is being measured, per second.
Current is measured in amperes and can be measured with most standard multimeters. One ampere is equal to 6.241×1018 electrons passing the point being measured per second.
If we think of electricity as water flowing through a pipe, the following diagram will help visualize what current is: