What causes gas pressure (in terms of kinetic theory)?

is caused by the collisions of gas particles with the walls of the container.
According to kinetic theory molecules inside a volume (e.g. a balloon) are constantly moving around freely.
During this molecular motion they constantly collide with each other and with the walls of the container.
In a small balloon that would be many thousands of billions of collisions each second.
The force of impact of a single collision is too small to measure.
However taken all together this large number of impacts exerts a considerable force on the surface of the container.
If they hit the surface of the balloon straight on (at a 90 angle) they exert their maximum force.
If they hit the surface at an angle less than 90 they exert a smaller force.
The sum of all these forces causes the pressure ##P_B## that is exerted by the gas.
The diagram above represents a balloon containing molecules of a gas (the red dots).
The yellow arrows indicate that the gas pressure ##P_B## in the balloon is exerted outward against the walls of the balloon.
The larger the number of collisions per area of the container the larger the pressure:
Pressure = ##Force/Area## or ##P = F/A##.
The direction of this force is always perpendicular to the surface of the container at every point.
The video below gives a good explanation of gas pressure.