What exactly is the difference between the Legislative Assembly and the Legislative Council ?
The earlier answer would be fine if the country of origin of the student posing the question was not relevant. Because the student is a national of India, however, that earlier answer is not particularly helpful. Like many countries, India is politically and administratively divided into a number of states, 29 to be precise. Like Great Britain, India's former colonial ruler, India's parliamentary structure is bicameral, including at the state level. While the United States Congress is bicameral, both the House of Representatives and the Senate share a great deal of power, with neither able to act completely independently of the other, with the exception of the Senate's power to confirm Executive Branch appointees. Both Great Britain and India, in contrast, have an upper and a lower house of parliament. In India, the lower house is the Vidhan Sabha, (or Lok Sabha) or Legislative Assembly, with a greater number of representatives than in the upper house, the Rajya Sabha, or Legislative Council. The Rajya Sabha, unlike the Vidhan Sabha, cannot be summarily dismissed by a state governor, and has fewer members bespeaking its less directly-representative nature. Members of the Legislative Assembly are directly elected by their constituencies; members of the Legislative Council are elected by the members of the Assembly. In other words, the Legislative Assemblies of each state elect that state's members of the upper house. So, the earlier answer is wrong in stating that members of the Legislative Council are appointed rather than being elected. As with the U.S. Congress, the consent of both houses is needed for the passage of legislation.
The earlier answer, as stated, is misleading by virtue of its neglect of the subject matter at hand. India's government was highly influenced by that of its former colonial ruler, Great Britain, and Indian law reflects those British influences. It is unfortunate that the student posing the question was poorly served by the previous answer.
Individuals are elected to the legislative assembly through a democratic process, while members of the legislative council are appointed. Because the legislative assembly is elected, individuals are more likely to stick with their party lines than individuals in the legislative council. This is to say that the legislative assembly is more partisan than the legislative council. The legislative assembly also has more power than the legislative council. The legislative assembly can introduce legislative bills while the legislative council can not, the legislative council is only able to delay bills and not stop them, and the legislative assembly has more control over the executive branch of the government. The purpose of the legislative council is to hold the legislative assembly accountable, and is thus able to delay bills in order to prevent bills from being passed without a proper inspection and understanding of the bill.