Along with the costumes, props help lend a sense of character to the figures using them. They become imbued with a bit of the figure's personality, and can even serve as a short-hand form of identification. Consider Indiana Jones's bullwhip, for example, or the broomstick Margaret Hamilton used as the Wicked Witch of the West. Both serve as indelible extensions of the character, and neither figure would be quite the same without them.
Movie props often go a long way towards conveying the time and place of the narrative. By using props corresponding to a particular period in history--such as a flintlock pistol in Colonial America or a bowl of grapes in Ancient Rome--that history comes alive more readily. Similarly, science fiction films make their far future settings more believable with props representing pieces of high technology. Fantasy films--even those set in the modern world--do much the same, bringing their magic to life with props that represent magical swords or necklaces.
The package of reality which props bring to a movie production serve as tools for the actors to get the feel for their role. An actor feels more like a gangster when he has a Thompson submachine gun in his hands, and the actors playing Jedi in the "Star Wars" films each had their own light sabres to give them a better sense of their parts. This is especially true in effects-laden movie productions which use a lot of green screen--where the surroundings are added by computer and the actor needs to use imagination to conjure the proper atmosphere.
Props can actively serve as fulcrums for the drama, allowing the plot to move forward from one scene to the next. They can also serve as overt symbols in the story, helping to convey its overall theme or subtext. Consider the box of chocolates which Tom Hanks holds as Forrest Gump--accentuating his speech about life--or the headpiece to the Staff of Ra in "Raiders of the Lost Ark," which Indiana Jones must find if he hopes to uncover the Ark of the Covenant.
In cases where the action calls for a weapon to be used, props can help ensure the safety of the actors. A fake gun or knife can look just as dangerous as the real thing without the attendant threat, while prop masters can create "breakaway" furniture which shatter harmlessly when broken over an actor's head.