Personal assistant job duties are different from job to job. It's impossible to give a set-in-stone description of what to expect because what personal assistants are asked to do will all depend on the needs of the employer. That being said, it is possible to say that most positions will cover a few standard areas, involving communicating with various individuals, taking care of paperwork, and solving problems that are logistical in nature.
One of the principal responsibilities of a PA is to deal with communications with clients, colleagues, associates and so forth on behalf of the employer. This means composing letters, making phone calls, and meeting with the individuals which the boss associates with. Over the course of their career, a PA will get to be highly proficient at selecting a suitable wording and tone according to the person being contacted in each situation. Someone who stands out in this area is going to be of great value to their boss.
The second most common personal assistant job duty is of course administration and paperwork. There tends to be a lot of scheduling that Pas are responsible for; to make sure that their employer makes all of his or her appointments and has a balanced amount of work per day and throughout the week. Note-taking is also important so a good PA needs to be able to keep up with their employer and jot down all the tasks that need to be completed. Often a personal assistant can delegate some of the more basic paperwork to receptionists and other individuals in order to get everything done.
Finally, there are frequently a lot of tasks that entail running errands and solving problems. This is especially true of a celebrity assistant, who may discover themselves in odd locations late at night trying to please their boss by filling a very specific request. A demanding employer might just drop problems onto their personal assistant's lap with the command to "fix it." This can lead to some resourceful solutions so as to get the required outcome.
The personal assistant job duties that get assigned will really depend on the needs of the employer. You could find yourself working for someone who needs many different tasks completed, or that have you running around at all hours in order to get results. You could find yourself working as one of the many on-call personal assistants who only do routine secretarial duties, like typing and answering the phone. Whether this is a good thing or not will depend on what each personal assistant is interested in and the kind of work they hope to find.