The proton, one of the particles which make up the nuclei of atoms, is thought to be composed of three smaller particles called quarks. In order to observe the structure of the proton, and verify this theory, scientists must use novel techniques to probe the tiny length scales involved.
An analogous problem is that of looking at the structure of cells from a living thing. To observe the structure of these cells, we look at them under a microscope. Here, optical effects allow us to magnify the image we see when shining light through (or reflecting light off of) a cell. The resolution (roughly speaking, how small a structure we can distinguish) is determined by the wavelength of the light used. The smaller the wavelength of light (higher frequency) the smaller the structure we can observe.
The problem of observing ever smaller structures has led to a great number of techniques in microscopy, surface imaging and related fields, but none of these are sufficient to look at the structure of the proton. At such a fundamental level, one must try something entirely different!
The properties of the electron, a small charged particle, are very well known. It is believed that the electron is what is known as a fundamental particle; that is, it is not made up of smaller building blocks. The electron is therefore used in a process called Deep Inelastic Scattering (DIS).
DIS involves firing electrons into protons and looking at what comes out. The inelastic part implies that the electron does not simply bounce off the surface of the proton, but breaks the proton up into its constituent particles.
The quarks inside the proton must be bound together into what is known as a colourless combination (each quark is given a colour, which is just a way of labelling a certain quantum number). In a proton, the three quarks make a colourless combination, and if one quark is pulled out of the proton, the energy associated with the strong interaction between the quarks increases linearly with the separation of the quarks. After a certain point there will be enough field energy between the quarks to create a new quark pair. This is the process that DIS looks for.
When the electron is fired into the proton, the quarks fly out as essentially free particles. Free quarks are short-lived because they rapidly produce quark-antiquark pairs out of the field energy of the strong interaction, and this results in a jet-like spray of new particles created; all going in the direction of the original quark.
These jets allow the paths of individual quarks to be reconstructed quite precisely, permitting physicists to study the immediate products of a deep inelastic scattering interaction, and thus to gain insight into the structure of the proton.
Electrons are used as the probe particle because they are not made up of anything smaller, so when the proton fragments, it is easy to determine which of the fragments is an electron and which fragments came out of the proton!