@Lion Lots of good information has been given on intention, but I would also like to expand a bit on Bardon's definition of intention. You will not see him define it specifically in Initiation into Hermetics, but in the Czech Hermetics translation of "An Aide to Introspection", there is a brief foreword that is written by Bardon. This foreword contains some crucial hints on how he defines intention and I think it will be quite helpful for you to consider these as keys to understanding what "intention" could be.
His hints are basically regarding the different ways to "impregnate" the air, food, or water with "wishes" in order to help with your elemental soul equilibrium practices. The different types of impregnations he mentions are:
1
. Intellectual impregnation - This involves either "speaking" your wish into the medium and letting the substance absorb your words. This is almost considered a physical level impregnation whereby you are infusing the intellectual meaning of the wish into the substance's akasha.
2.
Emotional impregnation - This involves projecting the emotions associated with the wish into your substance and is an astral level infusion to the substance's Akasha. Every wish you have also has emotions associated with it. For example, if you are wishing for tranquility, then you would infuse the emotion of calmness into the substance.
3.
Visionary impregnation - This involves using the imagination in order to conjure a visual representation of the wish and could probably be considered a mental level impregnation. Again if you are wishing for tranquility or to be a tranquil individual, then you would imagine a picture of yourself as an extremely calm individual. This could be you meditating in a calm environment, etc.
The key to understanding intention is to understand that these 3 impregnations are all components of intention. I think Franz Bardon associates the "wish" with "intention". So you need to ask yourself again, what is "intention"? It could be a wish, a direction, and a will towards something, such as a goal.
But what does it look like, practically? For some people, intention is a feeling / emotion combined with a visualisation of what they want. For some others, it is an intellectual understanding of what they want combined with emotions for that want. In many cases, an intention is all 3 things:
1. An intellectual understanding of what is wanted.
2. The intense feelings for that "want" or "goal"
3. A visual (or sensory) representation of what that goal looks like, which is likely closely related to the intellectual understanding.
With all 3 of these components, Bardon mentions that the strongest impregnation of the wish can be achieved into the substance and this will lead to the strongest level of manifestation across the different levels of existence (i.e. mental, physical, astral). And this also likely is what he considers the key for "intention" in magic. So I guess you could say intention is all 3 components of a will being applied in some direction.
In ceremonial magick, I feel this definition of intention is a very practical one to use. If you are evoking a spirit and you wish to allow the spirit to understand what you wish for, you may use a combination of speaking your wish (i.e. intellectualising it to the spirit), feeling the emotional strength of your wish, and mentally visualising the wish / result to the spirit. This will transmit a very clear picture to the spirit of what you are asking for. If you are using ceremonial magick to consecrate a talisman, then infusing the wish into the talisman in the same way as you would with the food / drink / air impregnations would probably be a logical choice.
You could apply this knowledge across different traditions beyond ceremonial magick of course. Many of the chaos magick definitions here would also fit quite well with this framework of course. But I feel like this definition from Bardon is the easiest to understand and actually addresses, component-wise, what exactly intention is.