There isn't one Heaven, each soul generates its own paradise.
– Castiel, 6.20 The Man Who Would Be King
God resided in Heaven with his angels until his departure sometime in the distant past. In God's absence, the archangel Michael led the angelic Host and directed the affairs of Heaven. Raphael was also an authority. The appearance of angels in Heaven is not necessarily human, even though they may be perceived in that manner by deceased souls. For example, Zachariah says that in Heaven he has six wings and four faces. Angels draw some of their powers - demonic exorcism, healing and possibly resurrection - from Heaven. Those who fall and are "cut-off" from Heaven are weakened, and are not allowed to return on their own. It is still possible for the banished to communicate with Heaven. Anna can hear other angels speaking, even without her grace. Castiel is able to communicate with Sam and Dean through a link to electronic equipment - such as a radio or TV - in their memories.
Heaven also serves as a destination for deserving human souls after death. They occupy the happy memories they experienced on Earth, reliving them in their personal Heavens. It is unknown how a human soul is allowed salvation in Heaven. Joshua suggests that it is on a case-by-case basis and can be God's decision; this is the case with Sam and Dean. Raphael says that if a person is devout, it can cover all sins.
Angelic society in heaven is arranged into a rigid, militaristic hierarchy. Each angel is a member of an Angel Garrison with its own supervisors who report to higher authorities. This arrangement has been breaking down since God's departure from Heaven. Following the imprisonment of Michael in Lucifer's Cage, Castiel describes the situation there as civil war. Garrisons now seem to be breaking up due to the conflict in Heaven.
The Axis Mundi is a path that runs through heaven. Different souls in Heaven see it as different things - For Dean it is "two-lane asphalt". According to Castiel, some view this axis as a river. The road will lead the traveler to Eden.
In mythology the Axis Mundi is the path between heaven and Earth, and is depicted symbolically in different ways in different cultures - from the Totem pole of American indigenous people to the Pyramids of Egypt and the Bodhi tree where Buddha found enlightenment Source.
In Heaven, humans occupy their happy memories, reliving them in their own, separate worlds. When Sam and Dean are killed and find themselves in Heaven, they move along the axis mundi from one happy memory to another - although the memories that are happy for one brother are not always so for the other. When they meet Ash, he explains that everyone has their own “heaven”, and at the center of all of them is Heaven's Garden (see below).
According to Ash, most people cannot leave their own “heaven”, although Ash had worked out a way to do so. He has also rigged a device that allows him to listen in to the angels. Other people Ash has met in heaven are Johnny Cash, Andre the Giant, Einstein, Pamela and Mallanāga Vātsyāyana who wrote the Kama Sutra. Ash has been unable to locate John Winchester.
Ash says that some or few people (Ash referred to these people as 'special cases' because of the rarity), for example, SoulMates - share their Heaven with each other. Sam and Dean appear to share the same "Heaven".
Angels have access to people's personal Heavens. Zachariah appeared in Dean and Sam's memories, and Adam informs Dean and Sam that the angels recruited him while he was experiencing a happy memory in Heaven. Angels can choose to spend time in the personal Heavens for their own reasons. Castiel enjoys an autistic man's Tuesday afternoon Heaven, which is a peaceful park scene, and Raphael uses Ken Lay's Heaven for meetings.
According to Ash, this garden is the core of Heaven, and is at its center. This portion of Heaven, according to Joshua, can be referred to as God's Throne Room or as Eden. Joshua is an angel who tends the Garden. Souls that travel to the garden, according to Joshua, will see it differently; for Sam and Dean, it is the Cleveland Botanical Gardens that they visited on a grade-school field trip.
Virgil watched and protected the Angelic Weapons before the angelic civil war. During the chaos after Michael's imprisonment, numerous powerful angelic artifacts were stolen by Balthazar, including the Staff of Moses and Lot's Salt.