Personal Reality

Although not has been disclosed on the true meaning of Personal Realities, it has been repeatedly stated it is the source of an Espers abilities

Function
Apparently, all human beings have a Personal Reality within their minds; specifically their consciences. It is possible to develope it individually, and will lead to that person attaining supernatural powers, therefore making them an Esper. The more powerful or more growth a Personal Reality becomes, the stronger the powers of the Esper are.

It seems that it is the source of an Esper's AIM field.

Development
It seems that there are multiple methods to give the Personal Reality growth. A commonly seen test is the use of Zener Cards where the student cannot see the cards, but must guess the right symbol.

It's growth is correlated with the brain's processing ability, and can become more powerful if there is a stronger 'processor', such as a result of Level Upper. If that processing ability is deterred (e.g Capacity Down), the power can either lose its strength or become unusable, such as in Accelerator's case after being shot or Kuroko's inability to teleport when she can't concentrate. As shown by Kiyama Harumi, if one controls another's conscience (and therefore his/her Personal Reality), they can access that person's powers.