Aap is most formal form of “you”. It is used to address an elder, stranger, relatives or used in official use. This form must always be used to address
an elder (formal or informal) and a stranger. It shows respect for a person. The respect apart, this form can show the distance between the people. In informal environment, it is understood that when a person continue to use “Aap” for a long time, he wishes to maintain a distance. In the Indian society, now days majority of parents are forcing their children to use “Aap” to address everyone including themselves. If you could speak Hindi and would be communicating with an Indian for the first time, you would have heard it already in your communication.
Tum is a less formal form of “you”. It is used in informal environment, among elder members in family, married friends , official environment among work colleagues etc. It shows that the people know each other and at same time, wish to give the respect due to age or environment. In Hindi, it is the most conservative address for “you” to address a familiar person. In familiar environment, if you are addressed with “tum”, don’t get nosy that you are now given a less respect. It is most likely that you are now more accepted in their circle, understanding or a relationship.
Tu is the informal form of “you”. It is used in an informal environment, close relationship and illiterate masses. It is also used to address God. It represent a close bond among the person and it is used by close friends, pre-marital couples, young family members, same age relatives etc. Its wrong use could be offensive and it is heard sometime in verbal fight or in high temperament.
This form has been used and still used by children to address their parents. Some parents are expecting their children to use “Aap” instead of “Tum” or “Tu”. To new generation, the use of “Aap” is valid in even in close relationship because it represent etiquette, manners and being civilized.
Though, the other people think that overuse of formalities are killing the essence of human bonding and everything that represent it. My personal opinion is with latter and I believe that “Aap” could be avoided in close relationship.