The Rifle is primarily used for defense against raiders, but can also be used for removing indoor threats. It is also required for a military event where the player is asked to dispose of it. The Rifle does not require the ammunition to work. As of the DLC update, it makes a reloading when clicked on and if the player brings it in an expedition, the character that goes in the expedition will have less of a chance to be captured by raiders.
The rifle is most likely a sporterized Springfield 1903, a common type of bolt action for the 1950's.
Events involving the rifle
Summary: Raiders come to the shelter and order the family to surrender. The rifle can be used to hold off the raiders without trouble.
Military Gun Event (Requirements: Rifle)
Summary: The military comes onto the radio and asks all current survivors to dispose of their firearms. This breaks the survivors' 2nd amendment's right to keep and bear arms. Using the Rifle will increase the chance to get the military rescue ending.
Summary: The family is about to go outside into the wasteland when a growling is heard in the shadows. Using the Rifle scares away/takes down Pancake and he is never mentioned again.
Whenever there are rats, bunny-beasts or roaches in the shelter, using the rifle will successfully take them down, but there's a chance that the rifle will break if the player chooses to use it.