Rutherford's atomic model is the most well-known of the various atomic model ideas, and is the most commonly taught in schools. Before the discovery of his model, the most common atomic model was the “Plum Pudding” model, which stated that an atom was composed of two main parts: A large, positively charged nucleus (The 'pudding'), and many small, negatively charged 'plums' that were randomly spread throughout the positive nucleus. The Pudding model was basic and helped people to understand why an atom had no positive or negative charge (Because the positive and negative parts balanced each other out).
Rutherford was conducting an experiment to investigate how an element would react to being bombarded with a certain type of radiation. He chose to use a sheet of one-atom-thick gold leaf for this experiment (Gold worked because it was a large enough element to still be visible as a single atom), which he suspended in front of a radioactive source. The specific type of radiation used was an alpha particle, which is a positively charged nucleus of helium, he chose this because it had a charge (Therefore it would react to the positive or negative parts of the gold atoms) and a larger mass than other forms of radiation (This made any reaction the alpha particle had to the gold easier to spot).
The radioactive source emitted alpha particles which struck the gold leaf. If the Plum Pudding atom model was to be believed, then some of the alpha particles should have passed through the gaps between gold atoms, while others would be reflected by hitting the gold atoms. Rutherford observed that there were instead three reactions, a few alpha particles passed through, a larger proportion were reflected, and some were deflected off their path of motion but still passed through the gold leaf. Rutherford's atomic model came from several deductions he made from these observations.
First, if the alpha particles passed through the gold leaf, then there must be gaps of empty space between the gold atoms. Second, if the alpha particles were reflected, then the gold atoms must contain a positively charged part, because two positive charges will repel one another. Third, if the alpha particles were deflected, then there must also be a negatively charged part to the gold atoms, because a negative charge will attract the positively charged alpha particles.
These observations told Rutherford that the Plum Pudding model was inaccurate. He used his results to deduce another model for the atomic structure. From his observations he saw that the number of reflected alpha particles was greater than the number of alpha particles that were deflected. This lead him to believe that atoms were again composed of two parts, a positively charged nucleus (As in the Pudding model), and a negatively charged part that, unlike the Pudding model, existed outside the positive nucleus.
Thus, Rutherford's atomic model was formed. He believed that atoms had negatively charged particles orbiting their positively charged nuclei, and also that there were empty spaces between atoms. This formed the basis of further research on the atomic model and is held up today as the perfect way of introducing learners to the ideas of atomic structures.