The aircraft in the video is a remote-controlled (rc) airplane. Why it can "hover" is simply:
The thrust generated by a big fan / rc-jet-engine is much higher than the weight of the plane.
If the force generated by the turbine is the same as the downward-force of weight of the airplane, it hovers.
By very carefully adjusting the thrust and placing the aircraft in this "nose-up" position, a skilled rc-pilot can hover the plane until the battery runs out or fuel gets low.
As example:
An aircraft that weights 10,000 kg's produces a downforce:
$$F=m\cdot g=10,000 \cdot 9.81 = 98,100N $$
To make this aircraft hover, you have to create a upward force of at least $98,100 N$. If you manage to do that and you can align the generated thrust / downforce perfectly on the Y-Axis, the aircraft will hover:
$F_{down} - F_{up} = 0N$, the two forces will cancel each other out and you don't have any movement in the Y-Axis.
However, if you have engines that create more thrust than the downforce, the following will happen:
$F_{down} - F_{up} \geq 0N$, that means the aircraft will climb vertically (On the Y-Axis).
The same principle applies to other "real" aircraft, like the Sea-Harrier:
It uses the engine to create a force facing upwards. Because the force is greater than the downward-force created by the aircrafts weight, the Harrier can land / takeoff vertically.
The hovering airctaft is controlled by a trust-vectoring fan / turbine. Controlling the plane with the "normal" surfaces is not possible, because the airflow over the controll-surfaces on the wing is to slow. Therefore, only planes with trust-vectoring capabilities COULD hover like the rc-plane in your question.