Gandalf is known as the wizard that guides the Fellowship through their journey until Moria, but he is actually much more than that. Gandalf is a Maia, or the equivalent of an angel. He and the rest of his order (Saruman the White, Radagast the Brown, Alatar the Blue and Pallando the Blue) were sent to help in the fight against Sauron. Gandalf is the wisest of the Maia.
Aragorn is a Ranger of the North. He is recruited by Gandalf to escort the four hobbits to Rivendell. When the fate of the Ring is decided, he again volunteers his skill to aid the quest. Along the journey, he is forced to accept his heritage -- the true King of Men.
Legolas is a prince from the Woodland Realms. He comes to Rivendell in order to represent the Mirkwood elves in the Secret Council. While in the meeting, friction between he and the dwarves from Erebor is noticeable. When the fellowship leaves, he volunteers both his racial abilities and his bow. He accompanies Aragorn and Gimli throughout their adventures during the War of the Ring.
Gimli is a dwarf from Erebor, also known as the Lonely Mountain. Being too young to join the Quest for Erebor (only 60 years old at the time) he was anxious to attend the Secret Council. During the meeting, old friction with Legolas (prince of Mirkwood) is revealed. When the fellowship departs, he goes with it. During the breaking of the fellowship, he goes with Aragorn and Legolas, with whom he must learn to get along.
Boromir is the son of the Steward of Gondor. He is also the commander of Gondor's armies. He is sent to the Secret Council for three reasons. The first is to discover if the Ring has been found, and if so, obtain the Ring for Gondor's use against Sauron. The second is to gather any other aid for Gondor's unending war against the power of Mordor. When the fellowship leaves Rivendell, he goes with them to attempt to get the fellowship to go through Gondor, and also to attempt to gain the Ring. Unfortunately, he is corrupted by the Ring, but dies nobly during the breaking of the fellowship.
Frodo is the nephew of Bilbo, the hobbit who found the Ring in the Misty Mountains. When Bilbo leaves on his birthday for another adventure, he leaves everything to Frodo. When Frodo learns he has the Ring, he is charged by Gandalf to take the Ring to Rivendell. On his way there, he picks up fellow hobbits Samwise (his gardener and best friend), his cousin on his mother's side Pippin, and Pippin's best friend Merry. At Bree, where they are to meet Gandalf, they meet Strider/Aragorn. He guides them through the Wilderness to Rivendell. When the Ring starts to divide the Secret Council, Frodo offers to take the Ring to Mordor to destroy it. With Sam's help, he accomplishes this.
Samwise Gamgee is, as his father and his father's father, a gardener for the Bagginses of Bag-End. When Frodo leaves The Shire to take the Ring to Rivendell, Sam is charged by Gandalf to help him. When Frodo leaves Rivendell for Mordor, Sam decides to keep helping Frodo with his burden. Loyal to a fault, Sam is there for Frodo through everything, even when he is told to leave.
Pippin is a troublemaker. As a Took, he is from an adventurous branch of hobbits. He meets up with Frodo and Sam as they are leaving The Shire while running away from a farm with stolen food. He and Merry decide to go with Frodo as far as Rivendell, and continue on with the fellowship after the Secret Council. At the breaking of the fellowship, he and Merry are captured by orcs. He must then help nations fight evil while Sam and Frodo finish the destruction of the Ring
Merry is Pippin's best friend, and often the instigator of trouble. Loyal to his friends and family, when he and Pippin meet up with Frodo and Sam, he helps them to Bree, and then to Rivendell. Also being adventurous, he goes with the fellowship on their quest to destroy the Ring. After his rescue from the orcs that capture him, he devotes himself again to helping rid Middle Earth of evil.