This is how Sripad Ramanujacharya explains the verse:
In whatever manner seekers of refuge think of Me, according to their natural dispositions and surrender to Me — I favour them by revealing Myself to them in the
form of their choice. Why elaborate more here? All those who are intent on attaining Me will certainly experience Me, with their own eyes and other sense organs in every
way they may desire. The sincere spiritual aspirants will certainly experience an epiphany, that is, my essential nature however indescribable and inconceivable by the
Yogins it may be.
And this is how Dhyaneshwar explains the verse:
I tell you, in whatever way they serve me, in the same way I favour them. All men are, by
nature, inclined to worship me. But, many deluded by ignorance think of me differently and imagine me to be manifold, even though I am one. They think of me, though one, as divided
and give me, though nameless, different names and speak of me, though indescribable, as
god and goddess. Although I am ever the same everywhere, they explain me in parts as high
and low, influenced by their confused thinking (66-70).
And this is how Sridhara Swami explains the verse:
There may arise the opinion that Lord Krishna is partial to those who take refuge in Him and disregards those who are more partial to fulfilling their desires with sense objects. To clarify this false assumption the Supreme Lord stated this verse confirming that by whatever mode or method a person worships Him, direct or indirect, full of desires or free from desires He rewards them proportionately. It should not be falsely speculated that the Supreme Lord Krishna ignores those who due to ignorance neglect Him and instead offer others worship in various religions and denominations. It is impossible for Lord Krishna to ignore or exclude anyone because all living beings are factually following His path in every respect. Thus He is worshipped directly by those who are knowledgeable and indirectly by those who are unknowledgeable and correspondingly to their worship He reciprocates to each.
And this is how Srila Vishvanatha Nath Thakura explains the verse:
“Your dedicated devotees consider your birth and activities to be eternal, but others such as jnanis, surrendering to you for the purpose of perfecting jnana or other goals, do not consider your birth and activities to be eternal.”
“In whatever way they worship me (prapadyante), also give them the fruits of their worship (bhajami) in a similar manner.”
The meaning is this. Those who think that my birth and activities are eternal and, having a particular desire for my respective pastimes, worship me, attain happiness. And I, because I am the Lord, can do, or not do, or do anything. But making them my associates, with them I appear and disappear in this world at the appropriate time, in order to give my birth and pastimes an eternal nature, favoring them at every moment, bestowing upon them the fruit of their worship, prema.
The jnanis and others who surrender unto me thinking of my birth and activities as temporary, and thinking of my deity forms as material – I throw those jnanis again and again into the noose of maya with its temporary births and deaths, and bestow upon them the sorrow of birth and death, the fruit of their worship.
But those jnanis who accept the eternal nature of my birth activities and consider my deity form to be sac cid ananda, an surrender to me for perfection of their jnana, I liberate thos jnanis, since they desire the destruction of their gross and subt bodies, and I give them the bliss of brahman. I bestow up them the desired result of their worship: the destruction of birth and death born from ignorance.
Therefore, not only devotees surrender to me, but rather everyone (sarvasah), all men, jnanis, karmis, yogis, and worshippers other than the devatas, follow my path. Jnana, karma and other processes are all my path, since I am the essence of all those paths.
And this is how Swami Chinmayananda explains this verse:
Attachment and aversion are not the weaknesses of the
Lord. He is a mass of Dynamism, the source of all
activities and achievements. We are given the equipment
through which we can, as we like, invoke this Infinite
Mind. If we rightly invoke and carefully use the
equipments, as a reward for our intelligent self-
application, we can reach the Goal of our activities. If we
misuse them, the very same Divine Force can be the cause
of our utter disaster.
The fuel strength in the petrol can be converted into horse-
power through the mechanism under the bonnet. We can
invoke the horse-power to reach our destination, or we
can easily dump ourselves into a mass of twisted
wreckage on the way-side and become a bundle of broken
bones. These accidents are caused by the carelessness of
the driver, although the strength and power with which
the car dashes down the embankment of the road is, no
doubt, supplied by the same petrol. But the strength in the
petrol had no attachment for those whom it guided home
safe. Nor can we say that it had a hatred for those whom it wrecked. With neither attachment nor
hatred, the petrol gives its power when invoked through
the mechanism of the engine, and how to make use of the
power depends upon us and our wisdom in employing it.
Similarly, here the Lord says, "I, AS LIFE, LEND MY
POWER TO ALL WITHOUT ANY PARTIALITY; IN
WHATEVER FORM THEY INVOKE ME, IN THAT
FORM I SERVE THEM." An electric plug in the house can
be made use of to hear a song over the radio, to cool
ourselves with the breeze of a fan, to boil water, to cook or
to warm the room with a heater; it all depends upon what
instrument we plug into it. It is never possible that
electricity flowing through the fan, of its own accord, can
start emitting fire or light. Similarly, the unmanifest
Eternal Force of Life can be invoked, and It shall fulfil all
"desires" through us according to the type of our
And finally, Adi Shankaracharya:
Yatha, according to the manner in which, the purpose for which, seeking, whatever fruit; prapadyante, they approach; mam, Me; aham, I; bhajami, favour; tan, them; tatha eva, in that very manner, by granting that fruit. This is the idea. For they are not seekers of Liberation. It is certainly impossible for the same person to be a seeker of Liberation and, at the same time, a seeker of rewards (of actions). Therefore, by granting fruits to those who hanker after fruits; by granting Knowledge to those who follow what has been stated (in the scriptures) and are seekers of Liberation, but do not hanker after rewards; and by granting Liberation to those who are men of wisdom and are monks aspiring for Liberation; and so also by removing the miseries of those who suffer- in these ways I favour them just according to the manner, in which they approach Me. This is the meaning. On the other hand, I do not favour anybody out of love or aversion, or out of delusion. Under all circumstances, O son of Prtha, manusyah, human beings; anuvartante, follow; sarvasah, in every way; mama, My; vartma, path, [The paths characterized by Knowledge and by action (rites and duties).] the path of God who am omnipresent. By ‘human beings’ are meant those people who become engaged in their respective duties to which they are qualified according to the results they seek. ‘If Your wish to be favourable is the same towards all creatures on account of the absence of the defects of love and aversion in You who are God, and You are there with Your capacity to grant all rewards, why then do not all, becoming desirous of Liberation, take refuge in You alone with the very knowledge that Vasudeva is everything?’ As to that, hear the reason for this: