Rutherford's scattering experiment was to bombard gold foil with alpha particles so as to investigate the structure of atom.
He found out that by bombarding alpha particles on the gold foil, most of the alpha particles passed through the gold foil without being deflected. Only a small proportion of the particles got deflected. Thus this showed that what made up the bulk of the atom was actually empty space (where the electron orbitals are) and there was only a small concentrated region of the atom, where positive charges were concentrated-the nuclei (which made up the bulk of the atom's mass).
Alpha particles are actually helium nuclei, having 4 nucleons and 2 protons.
They are positively charged (since they do not have any electrons), hence upon close proximity to the positively charged nucleus of the atom, these particles will be repelled and thus scattered, as like charges repel.
This experiment demonstrated that most particles passed through the foil completely undeflected, while a few were deflected at extremely large angles. This showed that atoms consisted of an empty space with a very dense core (the nucleus), thus debunking Thomson's plum pudding model.
Rutherford used alpha particles because alpha radiation had a range of about 5 cm in air, and its range in denser materials had been measured.
Alpha particles are small (only two protons and two neutrons) and yet have enough mass (4u) to be a suitable missile (lots of momentum!).
They are produced naturally by radioactive nuclides that are alpha emitters (small proton-rich nuclei) and so a steady supply was easy to obtain.