For any of the 'advanced' stuff they present to you at A-level, I would suggest you just memorise it for the exam and move swiftly on. Some of the topics they cover are almost impossible to explain without a stronger understanding in areas of maths and physics.
To keep it simple, I'll try to cover it in these images:
This is a model of a typical 'particle in a box' thought-experiment. Focus on models B, C and D because they're easier to understand. They're standing waves, which I think you should know about from the A-level syllabus. The walls of this box are not physical walls, but are barriers of infinite potential. For example, imagine a charged particle existing between two instantaneous electric fields that are impossible to push through, so that the particle would be forever confined to the space in between.
For this to be the case, and assuming the De Broglie hypothesis of all particles exhibiting wave-like properties, the particle wave must be such that its amplitude is zero at the edges of the box. Otherwise its reflection at the boundary would be somewhat chaotic. The same as standing waves.
However. See next image:
The reality of the barrier of potential is that it is not ever going to be truly infinite, and so some particles, given the correct circumstances, will be able to surpass the barrier. There are certain probabilistic aspects involved which I am yet to be taught myself, but that shouldn't really be a problem in explaining this.
The process of particles crossing a barrier like this is called quantum tunnelling.
Since the particle has passed the barrier, it will then exist in a new space and can be detected by some device that, when the particle is incident on it, will induce some small current.
By scanning across the surface of a material, some electrons will be close enough, or configured rightly enough, to escape the potential barrier and jump across to be detected by the device.
With all that in mind, hopefully this final description will make good sense: