I am a year 13 student so please keep your answers simple! I am having trouble understanding the Lorentz force; does the magnetic field affect the electrons or what?
In the context of the homopolar motor you can find lots of resources on the Internet: e.g. http://blog.first4magnets.com/what-is-a-homopolar-motor-and-how-does-one-work/
In electromagnetism an EMF can be produced by changing the magnetic flux through a conducting circuit. However you can also produce a "motional EMF" by moving charged particles in a magnetic field, via the Lorentz force.
The Lorentz force is exerted on charged particles (in this case, electrons in the conductors) as they move with respect to a magnetic field. The force is of size $qvBsin\theta$, where $q$ is the charge, $v$ the velocity, $B$ the magnetic field and $\theta$ the angle between the velocity and B-field. It is directed at right angles to the B-field and velocity.
This force can be used to generate an EMF or in the case of a motor where the EMF is supplied, the Lorentz force can be used to move a conductor.
Electrons such as all protons, neutrons, positrons, ... have magnetic moment(s). If a electron lay in a magnetic field this field will align this moment, such like every magnetic dipole will be aligned.
Now if the electron is moving into a magnetic field his magnetic dipole will be aligned too. But this alignment is accompanied by a gyroscopic effect. Gyroscopic effect means that every rotating body act again the force which try to align it. Because the electron has not a magnetic moment only but spins too the electron will be deflected. Since any deflection lets to a photon emission and this emission is directed against the gyroscopic effect so the direction of the magnetic moment of the electron more or less fall back in his previous orientation. Now the game starts again. Only the electron due to the photon emission loses energy, the velocity slows down and the path of the electron is a spiral. If to be precise it is a spiral made from "tangerine slices"