Why is my voltmeter reading current and voltage in the air?

the value especially goes up wen i swing the leads around real fast. my engineering teacher tells me that it is picking up an EM field. if he's right, i don't quite understand what an EM "field" is. when electricity flows through a conductor, it produces an electric field, and a SEPERATE magnetic field that travels perpendicular to that of the E-field. so what exactly is this EM "field"? is it the overlapping part?.... but if he's wrong about the EM field, then what is it?