Here are some images of AMT's 1/50 scale Shuttlecraft Galileo II from Star Trek TOS.
A shuttlecraft, in the Star Trek fictional universe, is a smaller type of ship, usually capable of atmospheric transport, detachable from a larger starship's shuttlebay. Its role on starships is analogous to the use of naval helicopters on modern warships of the present day, as shuttlecraft often possess their own weapons and intelligence capabilities, and undertake a variety of missions--such as scouting/reconnaissance, search & rescue operations, and on a few rare occasions to fly ahead of the mother ship to provide forward navigational sensory data, map a safe flight path, and to provide course corrections to the mother ship. Most starships have shuttle bays for the launching and docking of shuttles as well as to serve as vehicle hangars similar to the way large naval ships are often equipped with helicopter pads and aircraft hangars.
Additionally, shuttlecraft also serve as landing crafts since most starships are not designed to land on planetary surfaces or to even enter dense atmospheres. Although Starfleet personnel typically use transporters to teleport themselves directly to and from a planet's surfaces for away missions, they do occasionally rely on shuttlecraft when the destination is beyond transporter range, such as distant planets or space stations, or when atmospheric disturbances or other conditions prevent the use of transporters. Shuttlecraft are also frequently used for planetary and stellar surveys. When sent on a planetary survey, the away team will often transport themselves to the surface and leave the shuttlecraft in orbit. Then when the team is ready to depart, they can activate the shuttlecraft's transporters by voice command.
The USS Enterprise traditionally names its shuttlecraft after renowned explorers and scientists. The three original named shuttlecraft were Galileo and Columbus, which appeared during the original series, and Copernicus, which appeared in the Star Trek: The Animated Series episode "The Slaver Weapon". Galileo and Copernicus remained traditional names for USS Enterprise shuttlecraft among the many incarnations of that starship. During Star Trek: The Original Series, several episodes depicted missions for the shuttlecraft. It was shown performing planetary exploration and search and rescue in "The Galileo Seven", and carried out a survey mission in "The Immunity Syndrome".