While Rutherford was not the first person to discover radiation, he did identify several important concepts related to it. He distinguished radiation based on the type of particles that it emitted, breaking it down into alpha and beta radiation. Alpha radiation was absorbed by a metal sheet, while beta radiation could pass through a metal sheet. Additionally, Rutherford was the first to identify radiation half-life, which is the amount of time it takes for half of the atoms in a sample of a given element to experience nuclear decay. Technically, alpha and beta radiation take their names from the particles the nuclei emit, namely alpha and beta particles.
Rutherford's most famous discovery is the nucleus of the atom, specifically his discovery of protons. The experiment done to discover protons is known as the "gold foil experiment," and it was performed by Hans Geiger and Ernest Marsden in 1909, under Rutherford's supervision. The experiment involved shooting a beam of particles at a narrow piece of foil made of gold in order to see how the atoms scattered. From this experiment, Rutherford came to the conclusion that atoms must have a positive mass centered in their middle. In 1920, Rutherford proposed the name "proton" for the particles that create this positive mass.
Rutherford's discovery of the proton led to his conception of the atomic model, which we still use today. This model has the protons and neutrons of the atom densely packed in the middle (known as the "nucleus"), with the electrons orbiting around the nucleus. Rutherford was the first to postulate this theory, and it stood in opposition to the then widely accepted "plum pudding model," which was created by J.J. Thomson in the late 19th century when he discovered the electron.
Rutherford is also credited with being the first scientist to technically split the atom. In an experiment in 1919, he shot alpha particles at a nitrogen atom (atomic mass of 14) and successfully created a hydrogen atom (atomic mass of 1) with leftover protons. While this was not at the same level, it is the same basic principle of an atomic bomb, a concept which was later refined with the Manhattan Project during World War II.