Kadampa Precepts 9

"A teacher from the district of Kham asked the teacher Drom, "What are the individual meanings of the twofold egolessness?"
Drom replied, "From the crown of your head to the soles of your feet, you cannot find
anything which is 'I', even though you search and make minute inquiry with your mind. This is the egolessness of person. Understand also that the mind of the seeker is without natural existence - that is the egolessness of phenomena." 

This is not, by the way, the usual explanation, though obviously it has a validity of its own. 
it is a very basic, very standard Mahayana general teaching. You have, to begin with, the nairatmya, or anatma teaching of the Hinayana. That is to say that within the so called individual there is no unchanging element. That the so called individual consists of a series of events at different levels, a flow of phenomena, a stream of
consciousness, but not any element that doesn't change. There is no unchanging element enucleating all the rest, it is stream that flows on from instant to instant. So this is the teaching of egolessness in the Hinayana. 
What happened was that there was a Hinayana school, the Sarvastivadins that took this rather literally, not to say literalistically. They recognized that the so called individual consisted of effervescent dharmas or psychophysical events but they tended to regard these events themselves as something real. So they ended up
with a plurality of reals, they regarded the dharmas as actual existence.
Then the Mahayana made the point that they were not, that just in the same way as the individual was just pure flux so the dharmas themselves were also, at their level, pure flux. So they expressed this in their technical language by saying that the dharmas were also Sunyata. They referred, therefore, to the emptiness of things, things in the sense of dharma,dharmasunyata. And the Hinayana view of emptiness or egolessness they called pudgalanairatmya, or pudgalasunyata, the emptiness of the person. So they regarded the Hinayana teaching in its more developed form as a limited teaching. That recognized only the egolessness of the person but the Mahayana recognized the egolessness of the so called constituent elements of personality.
So just as the Hinayana resolved the person, the pudgala into the void, in the same way the Mahayana resolved the constituent elements of the person into the void. In other words they did not stop, they pushed on with the process. So this is called the two fold egolessness. 
But Geshe Drom gives a rather different interpretation, though a very good one, a teaching which is, as it were valid in its own right. 
He is saying, as it were, everything that you look at, everything that you see in yourself is egoless. It is changing all the time, it just consists of process without any subject of the process which exists apart from the process itself. But he is saying don't go on to make the mistake of thinking that the mind that sees all this is unchanging, that mind too is egoless. In other words don't alienate the perceiving consciousness from what it perceives, don't regard it as an entity in its own right.