Ok, Hume is often a toughy, but I will give you a little peek into his views on Personal Identity....
He (somewhat) argues that Personal Identity, as we commonly use the term, as it relates to "ordinary people", does not exist. At least not in the way that we think it does.
The key term here is "bundle of perceptions". He defines the identity of a person as nothing more than the totality of that persons perceptions, this bundle makes up the "identity" of that person. However, these perceptions are always in flux! There is no moment during conscious life where our perceptions remain constant through time.
This differs from any regular non-conscious object. He talks about the identity of objects being definable because they (for practical purposes) stay the same through time, so that if a person were to examine them today, tomorrow, or next week, they would still be the same object. The ways in which objects remain the same constitutes their identity.
But since the Identity of a Personality is the constituents of its Perceptual Bundle, and those constituents are always in flux...Personal Identity does not exist, in the same way, as other ordinary objects, and in a sense, could be said not to exist at all.
Hume quote about this:
"Thus the principle of individuation is
nothing but the invariableness and
uninterruptedness of any object, thro' a
suppos'd variation of time, by which the
mind can trace it in the different
periods of its existence, without any
hreak of the view, and without being
oblig'd to form the idea of multiplicity
Hope that helps at least a little!