In the parlance of solid-state physics, semiconductors (and insulators) are defined as solids in which at absolute zero (0 K), the uppermost band of occupied electron energy states, known as the valence band, is completely full. Or, to put it another way, the Fermi energy of the electrons lies within the forbidden bandgap. The Fermi energy, or Fermi level can be thought of as the energy up to which available electron states are occupied at absolute zero.
At room temperature, there is some smearing of the energy distribution of the electrons, such that a small, but not insignificant number have enough energy to cross the energy band gap into the conduction band. These electrons which have enough energy to be in the conduction band have broken free of the covalent bonds between neighbouring atoms in the solid, and are free to move around, and hence conduct charge. The covalent bonds from which these excited electrons have come now have missing electrons, or holes which are free to move around as well. (The holes themselves don't actually move, but a neighbouring electron can move to fill the hole, leaving a hole at the place it has just come from, and in this way the holes appear to move.)
It is an important distinction between conductors and semiconductors that, in semiconductors, movement of charge (current) is facilitated by both electrons and holes. Contrast this to a conductor where the Fermi level lies within the conduction band, such that the band is only half filled with electrons. In this case, only a small amount of energy is needed for the electrons to find other unoccupied states to move into, and hence for current to flow.
The ease with which electrons in a semiconductor can be excited from the valence band to the conduction band depends on the band gap between the bands, and it is the size of this energy bandgap that serves as an arbitrary dividing line between semiconductors and insulators. Materials with a bandgap energy of less than about 3 electron volts are generally considered semiconductors, while those with a greater bandgap energy are considered insulators..
The current-carrying electrons in the conduction band are known as "free electrons," although they are often simply called "electrons" if context allows this usage to be clear. The holes in the valence band behave very much like positively-charged counterparts of electrons, and they are usually treated as if they are real charged particles.