We can understand this using an idea called the Kinetic Model of Gases. Basically, let's assume that every molecule in the gas is a tiny, tiny snooker ball whizzing around the container. These 'snooker balls' can collide with one another and the walls of the container they are in.

Now, the speed of the gas molecules (snooker balls) depends on their kinetic energy. The more kinetic energy they have, the faster they are moving. And the faster they are moving the harder they must hit each other and the walls.

Increasing the temperature will mean that we supply more energy to the molecules of gas and therefore increase their kinetic energy and speed. They will collide off the walls of the container harder. This raises the pressure because the pressure on the walls is defined as the force exerted by the molecules on the container wall divided by area (the area bit isn't too important here). The pressure is getting bigger because the molecules are whacking the walls harder!