"Densities" are essentially developmental stages of an entity or soul. The term "density' refers to the density of light, or information contained within a given space. As we progress as beings of love and light, we increase in what we might call vibrational frequency and move through these stages.
Each density has a seven sub-densities, which have seven sub-densities, and so on. After proceeding through the 7th density of a system, an entity proceeds to the next "octave" of existence.
The 7 densities of our octave of existence are as follows:
1st Density - Awareness
All atoms, molecules, and energy in the universe has consciousness. Although these consciousnesses are not self-aware, they still perceive existence in their own way. They have their own experience, just like any other consciousness. For example, a molecule may trade electrons, repel other molecules, or combine with another molecule in order to expand to a greater consciousness.
2nd Density - Growth
In this stage, we start to see consciousness actively seeking to progress, "striving towards light and growth", as Ra states. He gives a simple example of a leaf striving towards the source of light. Once an entity has reached a point of self-awareness, they are "harvestable" for, or ready for graduation into, 3rd density. This is often-times greatly accelerated in the relationship we have with pets, where we help our domesticated 2nd-density family members to achieve a sense of identity. In that way, we are their 3rd-density mentors, teaching the lessons we have, ourselves, already learned.
3rd Density - Self-Awareness
This is the density of self-awareness, when an ego can start to make rational decisions that will carry consequences for that entity. It is for this reason that 3rd density is sometimes called "the choice". In this stage, each entity reaches a fork in the road, for to progress beyond 3rd density, the entity must "polarize", or head down one of two paths: the positive (service-to-others) path, or the negative (service-to-self) path. As we are all part of the same universal consciousness, to serve one's self is to serve all, however, the negative path of service to self is a difficult road. In this density alone, harvestability into the next density is dependent upon one's dedication toward the love and service of others or themselves. This must come from a place of love and understanding. Hence, those on the positive path radiate their love outward from their 4th (green-ray) energy center and serve those around them. Those entities who are on the negative path, instead close off their 4th energy center and project that love entirely inward, loving themselves and serving themselves through the manipulation and control of others. For this reason, the positive path is that of acceptance and the negative path is that of control. As 3rd density is for this choice, we are given a veil of forgetting so that we may more quickly polarize, for the choices made when certain catalysts arise are far more weighty under these circumstances.
4th Density - Love and Understanding
The 4th density is that density where entities have chosen a path of loving themselves or others and are now ready to progress in that light. In 4th density, the veiling of 3rd density has been lifted and an entity remembers all of his/her previous incarnations of previous densities. It is in this stage that an entire race will begin to develop their spiritual gifts and abilities to what would be thought of to us as a super-human level. Things like healing others with energy or speaking telepathically start developing at unprecedented levels, and eventually become commonplace. The race learns to completely put aside their fears and objections and, through vast amounts of love, opens their thoughts and experiences through telepathy to all others of the group. Over the course of millions of years of development, this race becomes so aligned that although each member retains his/her identity, the race begins to act as one entity, forming a "social memory complex".