In making any kind of application, applicants typically know what they want and why, whether the application is for admission to a
program, for research support, or for a job.
However, in making this application (or others later), you should consider
the reasons the program (funding agency, or employer) would want to select
you. Then, within the bounds of reasonable modesty, you must go about the task of
satisfying them as much as possible as to each of those reasons.
Specifically, what reasons might the PhD program to which you are applying
have for accepting an applicant? Here are a few fairly obvious items. You
may have information about your field or the specific program that would
generate more items. But it is crucial for you to think about this application from
their point of view.
(1) They want to be sure you have the necessary native ability, background
in the field, and perseverance to do the work to finish your PhD in a reasonable
length of time. Of course, they are allowed hope you will do important publishable research that will enhance the reputation of their program. So you should mention anything that involves success in your previous studies
or allied intellectual pursuits. (@JaganMohan has listed some items.)
(2) Possibly they will be guaranteeing you some financial support. This may
involve your being a teaching assistant (eventually possibly lecturer) or a
research assistant. So you should mention any work you have done reading student
homework or exams, any work helping students (US 'tutoring'), any proficiencies
for literature searches for research projects, experience using relevant lab equipment, and anything that gives evidence of relevant computer or programming skills.
(3) Work toward a PhD is not for everyone who does reasonably well as a BS or MS
student. Not everyone stays with it. They are limited as to how many people
they can admit, and they'd prefer to admit people who can stand stiff competition, can successfully manage a demanding workload, and who do not
get panicky or discouraged the first time things go wrong. So, mention of
nonacademic jobs you did to help with expenses, and any long term projects you have finished (even if not exactly in your field).
It is probably best not to speak directly to their motivations. They know what
they are looking for without your instruction. Simply give them information that will allow them to be satisfied on each point. Just lists of facts, don't exaggerate or psychoanalyze
yourself. If something seems too much like bragging (especially something difficult to document), maybe one of your references can do the bragging for you.