Cognitive Magic is a type of casting, along with Symbolic and Reflexive. This particular type relies upon mental willpower, and cognitive skills. It is built on how much energy the conscious mind can force out of the soul through sheer willpower, and forces the user to manually control what their energy does within the physical realm.
Therefore, such a style relying on so much mental power results in a weaker output of magical energy. An advantage of such a casting style is how precise it is, as the user is in control over every detail of their energy's actions as far as they think into it.
To properly apply apt Cognitive Magic, one must either possess great focused or must mentally become accustomed with performing a certain type of magic based off of pure will. Usually, one can utilized this class of magic in conjunction with Symbolic-- using the latter as a means of summoning the energy, then applying Cognitive works in order to manipulate the gathered mana.
The two main aspects of this particularly difficult genre of magic casting would be 'Power' as well as 'Control'.
As it pertains to power, the user is simply focusing on releasing either a high quantity of magical energy or force, low quantity, or somewhere in between. Usually, the first of the many options is utilized in order to increase destructive capability in combat. Furthermore, as one becomes more accustomed with forcing out particularly higher levels of power/energy, they usually can dial down the intensity for other tasks.
Control is a bit more crafty as it governs a broad range. For example, as a water magi, one could practice controlling the size of their 'Water Beam'. On top of this, the magi-in-training could simply proceed practicing how many different bodies of water they could manipulate at. Whether it's dictating the motion of your spells, the direction, the gathered quantity and so forth, all are pretty much govern by this aspect.
Both portions rely on mental ability, as stated above. Thus with enough practice, a sorcerer/sorceress could feasibly (for example) go from being able to control ten fire balls at once (with sleek and precise movements) to eventually being able to function the same, but with one-hundred fire balls.