It's common in media to allow inanimate objects the power of motion. Sometimes this is done for plot reasons. Sometimes this is done to add an element of surprise or the supernatural to a work. Whatever the reason, this trope is for when typically inanimate objects are self animated in a work.
When this happens, it is always obvious to the viewer and to any characters aware of the process. Depending on the object and whether there's a Masquerade going on, it might be obvious to everyone. Often objects that have this trope applied to them are anthropomorphized to a degree. Normally they are just given faces, but they may also be able to interact with their environment and hold things in ways that you wouldn't think a sofa would be able to.
How and why this happens varies from work to but there are some common variations:
They were always animate to begin with, but they often have to maintain a Masquerade. In that case this will generally hold true for all the same objects or to put it better the representatives of their kind.
They were made animate by The Power of Love or another strong emotion.
They absorbed some kind of Applied Phlebotinum, are Haunted Technology, or A Wizard Did It. (See also Instant A.I.: Just Add Water!.)
They are transformed biological lifeforms.
They are possessed.
They exist for a long time, such as 100 years. This is predominantly a Japanese concept.
Or the Rule of Funny is simply in effect.
Compare Companion Cube, which isn't animate at all but which is treated as if it was, and Animate Inanimate Matter and its subtropes, when instead of a discrete object it's a mass of normally inert matter. When they have a voice and fulfill a sidekick role to a bunch of humans, they're a Talking Appliance Sidekick.
These guys are also the main characters of Object Shows, to the point they're the trope namers.
Supertrope of:
Animated Armor
Anthropomorphic Food
Anthropomorphic Typography
Anthropomorphic Vice
Balloon of Doom
Books That Bite
Cumulonemesis
Eerie Anatomy Model
Egg Folk
Everything Dances
Golem
Living Clothes
Living Currency
Living Drawing
Living Dust Bunnies
Living Figurehead
Living Hat
Living Statue
Living Structure Monster
Living Toys
Sliding Scale of Living Toys
Vengeful Abandoned Toy
Love Imbues Life
The Man in the Moon
Monstrous Germs
The Old North Wind
Our Alebrijes Are Different
Snarky Inanimate Object
Sperm as People
Talking Appliance Sidekick
Talking Poo
Talking Weapon
Weapon Wields You
Sapient House
Sentient Stars
The Face of the Sun
Sinister Sentient Sun
Sentient Vehicle
Sapient Ship
Sapient Tank
Living Ship
Snowlems
Terrifying Tiki
Animate Inanimate Object has been suggested to play 3 roles. Click below to see other actors suggested for each role, and vote for who you think would play the role best.