The purpose of re-examination is clear from the bare language of Section 138 of the Evidence Act. It reads:

138: Order of Examination – Witnesses shall be first examined-in chief then (if the adverse party so desires) cross-examined, then (if the party calling him so desires) re-examined. 

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Direction of re-examination.—The re-examination shall be directed to the explanation of matters referred to in cross-examination; and if new matter is, by permission of the Court, introduced in re-examination, the adverse party may further cross-examine upon that matter.

Language of Section 138 of Indian Evidence Act, 1872

The first principles:

• While an examination in chief may be akin to building a wall, with bricks (of relevant facts/facts in issue), cement and all, cross examination is trying to punch holes into that wall and destroying its basis. Re-examination (which is what we discuss here!) is somewhat like trying to tell the Court that what appears to be damage to the wall or something that has displaced its basis – isn’t really damage (but a mere illusion of damage!) and can be explained away.
• Re-examination is optional.
• It is done by party who called the witness.
• Object: 
  • For the explanation of matters elicited/exposed in cross examination.
  • Clearing obscurities and confusion.
  • Putting new fact(s) which may have come out in cross-examination in correct/accurate perspective.
• Scope: New matters can be raised in a re-examination only with the permission of the Court, and on new matters, a fresh opportunity for cross examination is given to the opposite side. (this is fair!)
• Experience has shown that re-examination may be required when a confusing question is asked to the witness during cross-examination. For instance, a question such as “Have you stopped beating your husband ?” – is asked, and the witness ends up saying a simple Yes or No (because a clever cross-examining counsel may – sometimes – end up forcing the witness to answer in a plain Yes or No to a leading question). (*This is also an improper question and should be disallowed by the Court)
• It is clear that either of these answers may not be the correct answer, since she may be : unmarried, or less bizarrely, she may have never had any physical altercation with her husband. In such a case, to present the accurate and true picture to the Court, the witness should be re-examined and asked “What is your marital status?” or “Describe your relations with your husband”, or “Tell us I’ve you’ve ever had any altercations with your husband”. etc etc.
• Another illustration that may be a proper case study for utilisation of re-examination is : A witness being asked if the witness was wearing her eye-glasses at the time of the incident. (for instance, in case of a eye-witness to a Murder identifying the incident from a distance!). If the witness under the stress of cross-examination ends up saying No, then, something like this would usually be a very damaging circumstance that may make the court disbelieve her.
• Having said that, in such cases, she can and should be re-examined to bring out on the record that She was wearing contact lenses on that day (so not wearing her glasses was immaterial); or she’d got a lasik done right before the said episode, or anything else that helps build credibility to demonstrate that she indeed saw it happening.
• Therefore, re-examination is important in cases such as this, where the answer elicited in cross-examination – if allowed to stand on record – would paint a misleading picture or lead to a wrong inference in the mind of the judge.
• Having said that, a re-examination cannot be permitted to fill-in the lacunae/loopholes exposed in one’s case and for the witness to get another bite at the cherry and craft and give better answers.
• As you must have guessed by now, the need for re-examination may be considerably reduced by better and more pro-active exercise of powers u/s 165 of the Evidence Act by the Judge, where the judge puts questions to the witness with a view to arrive at the truth.
• Every trial, after all, is a voyage of discovery with truth being the ultimate quest.