It seems that some are still in their summer holidays
I will try to answer you, eventhough my English will not serve me a lot cause the subject needs the use of special jargon. Anyway, Ill try
Ijtihad may be considered as the fifth pillar of Islamic Law after the Noble Quran, the Sunnah (the prophet Muhamd (pbuh) practice, ijmaa (consensus), qiyas (analogical reasoning).
Ijtihad in Arabic means to work hard to achieve something beyond what others had achieved. In the Islamic Law, it means to try to make new reading of the legal sources, especially to find answers to new questions arised because of the new circumstances one live in, and find himself/ herself in delimma between his/her religion, and needs.
An example of Ijtihad was applied by Khalifa Omar Ben Khattab. According to the Quran, we have to cut the hand of the theif. This punishment has a lot of conditions to be applied. But, at the time of Omar Ben Khattab, there was a famine, and of cousre, theft spread, but Omar makes Ijtihad and he didnt applied the punishment.
There a lof examples, but unfortunately time isnt available.
Of course, the one who makes Ijtihad has to be a competent scholar, and his/ her Ijtihad shouldnt contradict the legal sources.