The material things around us are made of atoms. Atoms have a positively charged nucleus (the proton by convention has a positive charge), and the nucleus is surrounded by negatively charged electrons. Electrons are the mobile charges.
When we talk about negative charge, this really refers to electrons as Repetit mentioned. When one refers to a positive charges, in reality it means there is a lack of electrons. Natures tries to remain electrically neutral.
One can encounter positive charges, e.g. a free proton or ion, which one might encounter in atomic or nuclear physics, or in chemistry problems.
There are also positively charged electrons (positrons), but they occur under special conditions and do not survive very long.
However, when it comes to electricity/electronics, the negative charges are the electrons, and currents almost always refer to the movement of electrons. The current is always oppositve the motion of the electrons, because someone in the past decided that the direction of the current should be in the direction of 'positive' charges. I found that terribly confusing when I first learned about electricity.