If you ask me “self” is the same as what we call “ego”. An erroneous conception of a “self” that we believe to exist as some independent entity. In reality it is just a mental construct that allows us to navigate a body in a world interlocked by time and space.
If we want to explain a sentient being’s person/personality we could identify with one of the aggregates : “I am” a body, “I am” feelings, “I am” perceptions, “I am” thoughts, “I am” consciousness. When we identify with or cling to one of these aggregates, suffering arises.
The moment we realize there is no permanent “self” and everything is in a constant state of flux, everything is awareness experiencing manifestations of the mind, the self construct is not needed anymore.
Because of old views (memory) the mind may however reconsider a “me” to be existent (we can still consider each other to be separate entities, with different bodies, separate feelings etc.), but we shouldn’t, ultimately that’s a wrong view and creates all kinds of suffering. Instead meditate and just be awareness beyond concepts.
All is seeing colors, hearing sounds, smelling odors, tasting flavors, touching tangible objects, thinking thoughts, there is no “self”.
The Lankavatara Sutra, Chapter IV: Perfect knowledge or Knowledge of Reality helped me a lot:
The five Dharmas are: appearance, name,
discrimination, right-knowledge, and Reality. By appearance is meant that
which reveals itself to the senses and to the discriminating-mind and is perceived
as form, sound, odor, taste, and touch. Out of these appearances ideas are
formed, such as clay, water, jar, etc., by which one says: this is such and such a
thing and no other, this is name. When appearances are contrasted and names
compared, as when we say: this is an elephant, this is horse, a cart, a pedestrian,
a man, a woman, or, this is mind and what belongs to it, the things thus named
are said to be discriminated. As these discriminations come to be seen as
mutually conditioning, as empty of self-substance, as un-born, and thus come to
be seen as they truly are, that is, as manifestations of the mind itself, this is
right-knowledge. By it the wise cease to regard appearances and names as
realities.
When appearances and names are put away and all discrimination ceases, that
which remains is the true and essential nature of things and, as nothing can be
predicated as to the nature of essence, it is called the “Suchness” of Reality. This
universal, undifferentiated, inscrutable, “Suchness” is the only Reality, but it is
variously characterized as Truth, Mind-essence, Transcendental Intelligence,
Noble Wisdom, etc. This Dharma of the imageless-ness of the Essence-nature of
Ultimate Reality is the Dharma, which has been proclaimed by all the Buddhas,
and when all things are understood in full agreement with it, one is in possession
of Perfect Knowledge, and is on his way to the attainment of the Transcendental
Intelligence of the Tathágatas.