I see at least two correct answers here, however I get a feeling (based on the way the question was phrased) that it might be too complicated to understand this in terms of "valence/conduction bands overlap/gap".
The sentence you cited should be considered only in the whole context of the text. It does not make much sense standalone.
Let me try to describe the difference in simpler words.
The major difference between conductors and insulators is the amount of "free" conduction electrons - these electrons can be affected by the externally applied electric field, thus contributing to current flow.
- Conductors have many conduction electrons, therefore even low electric field (low voltage) can cause a large current. The other way to say the same thing is that the conductivity of conductors is high.
- Insulators have few conduction electrons, therefore their conductivity is low.
The definitions of "low" conductivity and "high" conductivity is heuristic, and it is possible that a material, which is a good insulator in one application, will be considered a conductor in some other application.
Most metals are very good conductors.
However, even an insulating material can be a very good conductor. Take an air for example - it is a very good insulator, but can become a very good conductor when the molecules are ionized. This ionization process and the subsequent conduction can be seen even by naked eye in forms of lightnings and sparks.
It usually takes a lot of energy to turn an insulator into conductor. This energy can be obtained from a strong electric field, high temperatures, etc... The exact amount of energy required is material specific (this energy is sometimes referred to as Band Gap energy). This brings us to semiconductors.
Semiconductors are insulators which require relatively low energies in order to "kick" the electrons to a conduction state. When electrons become "free", the conductivity of semiconductor rises. For example: semiconductor thermometer having an accuracy of 1\$^{\circ}\$C will change its conductivity in a measurable manner for temperature differences as low as 1\$^{\circ}\$C.
Energy, energy, energy... How is it related to the distinction between conductors and insulators? This energy, when transferred to "non-free" electrons, causes them to become a conduction electrons. This energy is used to "kick the electrons out of their permanent bonds" - once the electron is "kicked out", it becomes "free" and can be affected by electric field and contribute to current flow.
The above describes how do conduction electrons emerge in semiconductors, but there is one more mechanism which contributes to conductivity: when some electron is "kicked out" and becomes a conduction electron, it leaves an empty space behind (one empty electronic state in the vicinity of atom's nuclei). This state can be accommodated by another "non-free" electron "jumping" from its current position to this empty state. Why would it "jump"? Most importantly: due to external electric field which causes the electron to "want" to "jump".
The above "jump" populates the empty state, but creates another empty state in other place. You can see this empty state as "moving by himself". Since the motion of this state is in opposite direction compared to the "jumps" of the electrons, we can see it as being affected by the same electric field, but having a positive electric charge.
The above empty state which can "move around" under influence of the electric field and having equivalent positive charge is called a hole. Both negative conduction electrons and positive holes can contribute to current flow in semiconductors, therefore the latter are called bi-polar materials.
You can think of metals as having all the conduction electrons always present - no need to provide any additional energy in order to "kick" them to "freedom". Since no additional electrons can be produced in metals - no holes left behind. Therefore, in metals only electrons contribute to current flow, and you can say that metals are uni-polar materials.
Note that in both cases the only charge carriers are electrons. However, it is much more convenient to think of a positive hole moving towards (-) terminal, than thinking of many electrons "jumping" one after another towards (+) terminal. This should not be too hard for any electrical engineer since all of us are accustomed to treat the current as a motion of positive charges, neglecting the fact that these are electrons that in motion.
Hope this helps.