When current is flowing in a wire, what is actually moving is the electrons.
Electrons have negative charges.
Negative charge is usually shown in black, so in these illustrations electrons are represented as little black minus signs in little black circles. You have probably seen current shown as going from positive to negative, which isn't how the electrons move. Find out why current is usually shown from positive to negative. This applet was written by Lisa Denise Murphy at the University of Illinois. Early drafts were written in 1999.