There appears to be a 'self'
undergoing rebirth, but the ultimate reality is that there is no
real 'self' going through rebirth.
There is only rebirth, with no 'self' undergoing rebirth.
It is not easy to comprehend in the beginning, but the difficulty
is due to the limitation of the conceptual mind.
Nagarjuna used the eg of a waterfall. You see a 'waterfall', but
when you examine further, you cannot find a truly existing
'waterfall' that never changes. 'It' changes every moment, yet 'it'
is there. Actually there is no one truly existing unchanging
'waterfall' that exists there; there is only continous flowing, forming
the illusion of a 'truly existing entity called ' waterfall'.
Because there is continuity, we mistakenly think that there is a
thing called "waterfall" truly existing there.
Similarly, because there is continuity in our lives from moment to
moment and from live to live, we mistakenly think that there is
such a thing called a "real me" truly existing and undergoing
rebirth.
In the Milinda Panha, Ven Nagasena gave excellent replies to
questions by King Milinda.
(http://web.singnet.com.sg/~rjp31831/nagasena.htm#ID)
The king asked: "When someone is reborn,
Venerable Nagasena, is he the same as the one who just died, or is
he another?"
The elder replied: "He is neither the same nor another."
"Give me an illustration!'
"What do you think, Great King? When you were a tiny infant, newly
born and quite soft, were you then the same as the one who is now
grown up?"
"No, that infant was one, I, now grown up, am another."
"If that is so, then, Great King, you have had no mother, no
father, no reaching, no schooling! Do we then take it that there is
one mother for the embryo in the first stage, another for the
second stage, another for the third, another for the fourth,
another for the baby, another for the grown-up man? Is the
school-boy one person, and the one who has finished school another?
Does one commit a crime, but the hands and feet of another are cut
off?"
"Certainly not! But what would you say, Reverend Sir, to all
that?"
The elder replied: "I was neither the tiny infant, newly born and
quite soft, nor am I now the grown-up man; but all these are
comprised in one unit depending on this very body."
"Give me a simile!"
"If a man were to light a lamp, could it give light throughout the
whole night?"
"Yes, it could."
"Is now the flame which burns in the first watch of the night the
same as the one which burns in the second?"
"It is not the same."
"Or is the flame which burns in the second watch the same as the
one which burns in the last one?"
"It is not the same."
"Do we then take it that there is one lamp in the first watch of
the night, another in the second, and another again in the
third?"
"No, it is just because of the light of the lamp shines throughout
the night."
"Even so must we understand the collocation of a series of
successive dharmas. At rebirth one dharma arises, while another
stops; but the two processes take place almost simultaneously (i.e.
they are continous). Therefore, the first act of consciousness in
the new existence is neither the same as the last act of
consciousness in the previous existence, nor it is the
another."
"Give me another simile!"
"Milk, once the milking is done, turns after sometimes into curds;
from curds it turns into fresh butter; and from fresh butter into
ghee. Would it now be correct to say that the milk is the same
thing as the curds, or the fresh butter, or the ghee?"
"No, it would not. But they have been produced because of
it."
"Just so must be understood the collocation of a series of
successive dharmas."
Just as the flame of a candle. At moment 1, the 'flame1' is a
production of the candle, the oil, the wick, the oxygen etc at
moment 1.
At moment 2, the 'flame2' is the production of the candle oil wick
etc at moment 2.
At moment 3, the 'flame3' is the production of those conditions at
moment 3.
Each of these conditions are changing at every instant. Eg. the
wick is shortening, the oil is depleting, the candle's mixture of
elements have changed. So since these conditions have changed, the
'flames' have also changed.
Therefore, there is no one 'flame' existing throughout the night.
There is only a succession of dependently arisen 'flames', which
instantaneously arise and simultaneously cease, in a continuous
fashion.
... flame 1 - flame 2 - flame 3 - flame 4 - ...
This is analogous to our experience of 'self'.
There appears to be a 'wanderer' that existed since age 1 till age
20.
However, 'age 1 wanderer' liked toys and 'age 20 wanderer' liked
books.
'age 1 wanderer' had small hands while 'age 20 wanderer' has big
hands.
'age 5 wanderer' wanted to be a teacher while 'age 20 wanderer'
hated teaching.
now which is the real 'wanderer'?
while 'wanderer' recalls a continuity of growth from 'wanderer 1'
to 'wanderer 20' and so on... there is no one truly existing
'wanderer' that grew up.
from wanderer 1 to wanderer 20, all the instantaneous moments of
the 'wanderers' are merely dependently arisen, based on the coming
together and falling apart of temporary causes and conditions.
These causes and conditions, sometimes also known as karma, provide
the force that continually brings about birth-death... This forms
the illusion of a 'self' undergoing rebirth.
Your question of why some people can remember their past lives -
it's because even though there is no 'self' truly existing, there
is continuity due to the continuous occurrence of karma. Under
particular circumstances, with the right conditions, people are
able to have a glimpse of what happened in 'their' past
lives.
It is just like when you sleep last night and you woke up this
morning, you remember what happened to you last night. However, if
you analyse the 'you' yesterday and the 'you' today, you realize
that there is no real 'you' that slept through the night and woke
up in the day, but there is a continuity of a dependently arisen
temporary 'you before sleep' to the dependently arisen temporary
'you while sleeping' to the dependently arisen temporary 'you
awake'.
*Phew* very lengthy. 
Hope it helps to
clarify and doesn't create even more confusion.
This is a very impt qn in Buddhism. Thanks for raising it.
