A simplistic explanation that I have found useful is in “An Ascension Handbook” by Tony Stubbs which outlines the following viewpoint:

Your physical body exists in the 3rd dimension – it is matter-based. The 4th dimension is the astral plane – it is emotion-based. There is a belief that only in these dimensions can the illusion of good and evil be maintained and people can feel separated from Spirit and from each other. This is known as the Lower Creation World. This earth is now thought to be in a state of ascension. This means it is vibrating on the dividing line with the 4th and 5th dimension which is the Light body dimension where individuals become aware of themselves as multidimensional beings. Many seek greater understanding of their Soul purpose and many come from this plane to work as Lightworkers helping others to attain a greater awareness of their power within. The 5th dimension is the start of the Mid-Creation Realm where people are completely spiritually orientated, are engaged in spiritual trainings and readings and wish to offer service to others expanding planetary consciousness. We are multi-dimensional beings that are 3rd dimensional in human form, 4th dimensional at the level of ego and 5th dimensional as spiritual beings. The 5th dimension is accessible to us through visualisation and intention whilst we remain grounded in our human body.

The 6th dimension holds the templates for the DNA patterns of all types of species and is made up mostly of colour and tone. Consciousness creates thought here and this works when we sleep. Spirit Guides often act from the 6th Dimension. The 7th dimension is that of pure creativity, pure light, and pure tone. Pure geometry, and pure expression, angels have been said to act from here. The 8th dimension is of group mind or group soul and where you would touch base with the vaster part of who you are. It is characterized by loss of sense of the “I”. When you travel multi-dimensionally, it is this plane where you have most trouble keeping your consciousness together because you are pure operating with group goals. So, it may seem as though you have gone to sleep or, blanked out. The 9th dimension in the model that we use is the plane of the collective consciousness of planets, star systems, galaxies, and dimensions. Once again, it is very difficult to get a sense of “I” because you are so vast that everything is “you”. Every life-form, every star, – planet, and group mind of every species is you. If you visit this dimension, it can be difficult to remain conscious. The 10th through 12th dimensions make up the Upper Creation Realm. The 10th dimension is the source of the Rays. This is where Light is differentiated and is the source of plans of creation which are sent to the Mid-Creation levels. You can have a sense of “I” at this level but it won’t be what you are used to here. The 11th dimension is that of pre-formed Light, the point before creation and a state pleasurable expectancy just like the moment before sneezing . It is the realm of the being known as Metatron, and of Archangels and the Higher Akashic for this Source-system. There are planetary Akashic records and galactic Akashics as well as the Akashic for an entire Source-system. You are in one Source-system of many. There are other universes with different systems.

The 12th dimension is the One Point where all consciousness knows itself to be utterly one with All That Is. There is no separation of any kind. If you tap into this level, you know yourself to be completely one with All That Is, with the creator force. If you tap in there, you will never be the same again because you cannot sustain the same degree of separation if you have experienced complete unity.

Spirit creates the illusion of separation up to the 7th dimension. At higher frequencies, distinctions become completely meaningless, and all is Spirit.