As per Hinduism, the life on earth is not a discrete one time event. It is just one episode in the play. There would be multiple appearances (births) before the soul finally takes leave from the cycle. The birth is not just limited to being born as human, it includes the births as the animals, plants, even as the divines who rule the parts of nature ! After-all, all these things have a life. The appearance of the soul in any of such forms is called reincarnation. After so many births when the soul is freed of any more reincarnation, it is in the state of mukti or liberation. This is the ultimate state.
As the soul moves from one body to another, it carries forward something along with it, which is nothing but what it has accumulated performing various deeds. This can be thought of as a global account that each soul is associated with, irrespective of the place it is in currently. This account would have both the logs of good and bad deeds it performed similar to the credit and liabilities. This account is what is called karma.
This karma is further categorized. In the example let us assume the person on moving to the new place gets a new local account into which initially some of the credits and liabilities from the global account get transferred to start with. Subsequently till the person is in that location the day to day transactions occur onto that local account. Similarly from the global account of karma, which is known as prArabdham, some portion is transferred to the new local account when the soul reincarnates into a new body and this portion of karma is called sanchitham. In the day to day affairs the soul enjoys the fruits of the good deeds from the karma bank and suffers the fruits of bad deeds. In the process due to the deeds it performs the soul accumulates new good and bad karma to add to its account. This newly earned karma is called AkAmiyam. When the soul leaves that body the balance gets transferred back into the global account. The journey goes on.
In the life we see in this world, we work to get the results. The work is the action and the result is fruit of it. This is exactly what is karma. The fruit may come in a minute in a day, in a week, in a year or much much later that the delay may even make one forget the action that triggered the fruit got ! If there is no correlation between the action and the fruit, won't the world be in a mess ?! This theory would also explain why unexpected things happen - either good or bad. (As the situation undergoing due to the function of various past deeds.)
The reincarnation (in conjunction with karma) explains why some people never gets to see the fruits of their action in their life time and why some children die when they have committed no sin. When the karma exist one would have to undergo the fruits of it for which one may have to go through multiple births in multiple forms - plants, animals... The bank doesn't let you go unless the account is settled !
The discussion above may give raise to lots more questions - How did it all began ?, How would it end ? What is the relevance of God if everything as per karma ? .... Those who want to pursue these kind of questions can seek the answer from the Hindu philosophical paths of shaiva siddhantha(1), pratyAbinya (kashmira shaiva) (2), shankara advaita (3)...
When like the seed that is boiled out does not give raise to the plant, when the two types of karma (good & bad) nullify each other, You were there showing Your Measureless Form of bliss. - thiruvAsakam.
The well being of the people of ill-motive and the apathy of the good people are thought about. - thirukkuRaL
(Meaning it is the old karma that influences their state.)