This question is asked by the interviewer to know more about you. Your answer will tell the interviewer how best you fit for the job at hand.
Your strength can be good interpersonal relationship skills and weakness can be that you are not a self learner. You need someone to teach you. But you can tell your interviewer how you trying to improve by enrolling yourself in organizations like Jaycees or student development clubs which makes you aware of your hidden potentials. This will touch the interviewer. Be true to yourself while answering questions. Do not pretend to be some one else. If you falsify your dignity it might get you the current job but you will not enjoy doing the job and it will effect your efficiency.
Everyone has got weakness but that does not mean that we do not have have qualities. Describe your strengths with full confidence. Every person in this whole world is earning just by enhancing his strengths and working on the weakness. Do not try to show your strength as your weakness. Try to be true. Do not amplify your weakness or it will dwarf your strengths. Explain and move on.
For example if you have got good communication skills and you apply for a customer relationship management job, you are more likely to get the job. Your other weaknesses falls short. Always remember that you should have good communication skills and you should be able to convey your thoughts to the interviewer.
If you are applying for a sales job and love traveling and can maintain good interpersonal relations than the job is for you. Always remember the interviewer is conducting interview to select someone who can do good work and he is least bothered about other things.