I am not sure how specific of an answer you are expecting, but when they partitioned India, they decided to separate the Hindu and Muslim states into two separate countries, India and Pakistan. That went relatively well for most of the states with two major exceptions: Punjab and Bengal. Those two states did not had a clear majority so they decided to partition them as well so that they would join the right country.

Gandhi and some of the INC wanted a unified India but the Muslim party and Muslim extremists thought it to be a bad idea to have a state with a strong Hindu majority and a Muslim minority. They convinced Jinnah, one of if not the most influential Muslim politician of the time, to join their cause and the British thought it was the best plan of action.

This was a cause for tension between the two religious group. The Muslim didn't trust the Hindu and the Hindu where kinda still bitter at the Muslim for over 500 years of Mugal occupation.

When independence day came, a lot of families had to relocate on the other side of the border. Most of the people where illiterate and had no real grasp of what was going on. Families that did not want to move where persecuted and something killed by locals that wanted to grasp the land and farm for themselves. Of course they blamed the other religious groups for those forced resettlement. Clash where common thing and persecution would endure for years.

Religious extremist group on both side where exacerbating those tensions, calling for violence and accusing the people that collaborate of being traitors. Gandhi was not in Delhi for independence day, he was in Kolkata with a notorious Muslim crime lord who was responsible for the massacre of Hindu on multiple event. The transition in Bengal went relatively smoothly because of that. In the Punjab, things went sour. As the partition was happening, people jumped at each other throats and a lot of people died.

The Sikhs where not really taken into account and saw their land cut in half. They where also not happy.

On a side note, the state of Kashmir was a kingdom with a Muslim majority and a Hindu ruler. He was asked to chose his side. He thought that he could avoid that choice and that he would inherit an independent country. That didn't happen. Come independence day, Pakistan decided to invade the state to protect it's Muslim subject and achieved to invade a third of it's territory. India grabbed the rest of it under assumption that it had a Hindu ruler thus it should be part of India. They are still fighting over the legitimate ruler of Kashmir to this date.

On another side note, Gandhi was killed by Hindu extremist because of his affection for the Muslim. They saw him as a traitor. Ironically enough, killing him got them the hate of the public and made them weaker.

In addition to what /u/Kbek has mentioned, I should add that Lord Mountbatten assumed the armies of what were to be Pakistan and India would manage to prevent violence during partition. However, the armies refused to prevent the communal violence and instead supported their respective communities despite being under the command of English officers.

There is a good BBC documentary on the partition that might answer some of your questions. It has interviews with people who where there which explains their fears and motives on the violence.