Some people believe that mantras have an inherent power and make things happen magically. Though there is some truth to it, it is not entirely accurate.
Mantra literally means “that which shields/protects mind”. There are 3 types of benefits from mantras: (1) Mental discipline, (2) Material results, (3) Spiritual progress. Let us look at how each comes.
As repeating mantras with some level of focus engages the mind and protects it from harmful activity, it is clearly a tool for disciplining the mind and channeling mind’s abilities and powers.
Repeating different mantras creates different vibrations in mind. Normally mind vibrates with thousands of thoughts in addition to the mantra one is chanting. Though vibration of a mantra may not completely eliminate other vibrations, it will dominate them after some practice.
As that happens for a sufficient duration, the power of that mind gets channeled through that vibration. That may bring some material results.
It must be remembered though that the power is in the mind and not the mantra. Mantra just channelizes that power.
Suppose a chaotically flowing river floods surrounding villages often. Suppose we construct a dam and hold that water in a big reservoir. It avoids the flood and allows us to use the water better. Mind is like a chaotic river and mantra is like the dam!!
Of course, the dam has to be strong enough. Similarly, one has to be do enough sadhana to generate force needed to channel the power of a mind.
Will mantras give material results or spiritual results?
It depends on the mind that is doing the mantra. Even if someone pretends to oneself that one only wants “spiritual progress”, there may be some material desires hidden in the layers of mind. Then mind will work on fulfilling them.
As the power of a mind gets channeled, mind tries to fulfill its desires. But then, world is filled with many minds with many desires. And each desire has a different force behind it, determined by the intensity of the desire and how well the power of the desiring mind is channeled. Depending on the balance between various forces, some of one’s desires may be fulfilled.
As one makes more and more spiritual progress, overcomes desires (not at the level of external pretension, but at the level of inner reality!) and develops surrender to Lord, one’s mind becomes more stable. Things that normally excite, irritate, repel and scare one do not shake that mind that much. Such a stable mind catches the vibrations of mantras better.
Such a mind has a lot of power to fulfill any desires, but ironically it has far fewer desires than us. This is a stabilizing negative feedback loop that Nature has created - it makes it easier for one with very few desires to fulfill them!
How important are rules and technicalities, when it comes to fulfilling material results?
After all, using the dam analogy above, dam needs to be constructed well and water needs to be taken from the reservoir efficiently. Similarly, many rules were designed to maximize the ability of a mind to channel its power.
Various deities are personifications of different powers of mind. Though they are all essentially Brahman, Brahman manifesting as different deities and beings has different agendas, likes and dislikes. That cannot be ignored. Thus, there are some rules designed to maximize the ability of a mind to tap into any of its powers.
However, our understanding of the purpose/essence of rules is mostly corrupted. So most of us end up following the letter and not the spirit.
If one has a guru or mentor that one has faith in, one may follow the rules set by him, whether or not they make sense. Even otherwise, it is better to follow rules as far as possible, instead of taking a chance or letting guilt or apprehension distract the mind.
Though all rules can eventually be transcended, that has to be happen through sattwa and not through the tamas of laziness.
If one has a desire, it is better to accept it and work towards fulfilling it even while trying to genuinely (not just for pretension) overcome the desire by surrendering to Lord or at least transform it into something less self-centered and more expansive. One can make progress through a combination of honesty, sense of purpose and unshakable clarity about the end goal.