If a whole red heart is picked up and Isaac only heals half a heart container, the other half is placed in the jar, indicated by the jar number increasing by one. Despite the jar indicating that it picked up a whole red heart in this fashion, it will only drop half a red heart on use. When picking up a double red heart, the jar will also store the remainder not healed in the same way.
Co-op babies, except Magnet Baby, cannot add hearts to the jar, as they are unable to interact with pickups.
The short-lived half red hearts dropped by Tainted Magdalene can be picked up and stored.
The item only costs 10 cents when found in a Shop.
Synergies
The Book of Belial + Birthright as Judas / Dark Judas: Instead of dropping hearts on the floor, using The Jar consumes up to one full heart in the jar at a time, giving a temporary +0.66 damage up for each half heart consumed and spawning a puddle of red creep that deals 2 damage per tick (20 damage per second).
Book of Virtues: Consumes stored hearts to spawn heart wisps, rather than releasing heart pickups. Heart wisps have a chance to drop a Half Red Heart when destroyed.
Humbleing Bundle / Maggy's Bow: Spawn double the hearts put into the jar, allowing for infinite health to be spawned.
Mom's Locket: Any half red hearts stored by The Jar will be converted to full hearts when dropped on the ground. Since The Jar will store any leftover health from healing Red Heart Containers, this can allow for potentially infinite health when healing half-empty containers. Especially effective in conjunction with Cancer or The Wafer.
Interactions
Broken Remote: Allows for teleportation with no recharge; however, it drops the contained red hearts in the room it was used.
Car Battery: The Jar acts as usual, and doesn't double the hearts dropped upon activation.
Schoolbag: The player cannot pick up extra hearts while The Jar is in the inactive slot.
Shard of Glass: Storing a heart in the jar does not stop the bleeding effect, despite playing the "heart collected" sound effect.
Keeper/Tainted Keeper: Hearts of any type turn into Blue Flies upon spawning, rendering the item useless.
3DS The icon of The Jar as seen on the lower 3DS screen.
Trivia
The Jar is a reference to the Empty Bottles of The Legend of Zelda, which The Binding of Isaac takes heavy inspiration from. In Zelda, empty bottles are recurring items that are used to store a variety of items; this includes life-restoring items such as potions or fairies, which The Jar mirrors by allowing the storage of red hearts.
Red Hearts in The Jar if there are no remaining empty Heart Containers.
Super Secret Rooms that contain nothing but a 
Black Heart or 
Eternal Heart (Room ID's 1 and 6), it will spawn those types of hearts instead.
Tainted Magdalene can be picked up and stored.
The item only costs 10 cents when found in a 
Shop.
The Book of Belial + 
Birthright as 
Judas / 
Dark Judas: Instead of dropping hearts on the floor, using The Jar consumes up to one full heart in the jar at a time, giving a temporary +0.66 damage up for each half heart consumed and spawning a puddle of red creep that deals 2 damage per tick (20 damage per second).
Book of Virtues: Consumes stored hearts to spawn heart wisps, rather than releasing heart pickups. Heart wisps have a chance to drop a 
Half Red Heart when destroyed.
Humbleing Bundle / 
Maggy's Bow: Spawn double the hearts put into the jar, allowing for infinite health to be spawned.
Mom's Locket: Any half red hearts stored by The Jar will be converted to full hearts when dropped on the ground. Since The Jar will store any leftover health from healing Red Heart Containers, this can allow for potentially infinite health when healing half-empty containers. Especially effective in conjunction with 
Cancer or 
The Wafer.
Broken Remote: Allows for teleportation with no recharge; however, it drops the contained red hearts in the room it was used.
Car Battery: The Jar acts as usual, and doesn't double the hearts dropped upon activation.
Schoolbag: The player cannot pick up extra hearts while The Jar is in the inactive slot.
Shard of Glass: Storing a heart in the jar does not stop the bleeding effect, despite playing the "heart collected" sound effect.
Keeper/ 
Tainted Keeper: Hearts of any type turn into Blue Flies upon spawning, rendering the item useless.
The Binding of Isaac: Rebirth
