Why is an air intake located on the root of the tail on some aircraft?
That is the Ram Air Inlet for the air conditioning system:

Ram air, taken from the air scoop in the base of the vertical fin, is used as the cooling medium for  the  heat  exchangers.  Ram  air  passes  across  the  precooler  and  the  dual  heat  exchangers, extracting heat from the bleed air used by the air-conditioning packs. The ram air is discharged through exhaust louvers on the upper left and right sides of the aft fuselage.

During unpressurized flight, ram air may be used to ventilate the cockpit and cabin.

(Bombardier Challenger 605 - Air Conditioning &amp; Pressurization)
The reason why it is located there is obvious from the picture above: the two air conditioning units (ACUs) are located just below so this provides the shortest duct. For tail mounted engines, this is the optimal location for the ACUs (also called PACKs) because the bleed air ducts from the engines (or APU) can be short this way. The ram air can also be used for ventilation when the pressurization has failed.
For wing mounted engines, the PACKs are usually located in the belly. The inlets are then found on the underside of the aircraft:
What exactly are those openings in the bellies of many jetliners?
On some turboprops you can also find them on the side:
What&#39;s this hole on the ATR-72?