The Sensex is an "index". What is an index? An index is basically an indicator. It gives you a general idea about whether most of the stocks have gone up or most of the stocks have gone down.

The Sensex is an indicator of all the major companies of the BSE.
The Nifty is an indicator of all the major companies of the NSE. 
If the Sensex goes up, it means that the prices of the stocks of most of the major companies on the BSE have gone up. If the Sensex goes down, this tells you that the stock price of most of the major stocks on the BSE have gone down.

Just like the Sensex represents the top stocks of the BSE, the Nifty represents the top stocks of the NSE.

Just in case you are confused, the BSE, is the Bombay Stock Exchange and the NSE is the National Stock Exchange. The BSE is situated at Bombay and the NSE is situated at Delhi. These are the major stock exchanges in the country. There are other stock exchanges like the Calcutta Stock Exchange etc. but they are not as popular as the BSE and the NSE.Most of the stock trading in the country is done though the BSE & the NSE.

Besides Sensex and the Nifty there are many other indexes. There is an index that gives you an idea about whether the mid-cap stocks go up and down. This is called the "BSE Mid-cap Index". There are many other types of indexes.

In other word Nifty can be brief as: Nifty is an index or an indicator of the performance of the companies listed in national stock exchange situated in delhi. Nifty constitutes of 50 companies and the change in the Nifty index ( Up or down ) indicate the trend in the majority of the stocks. Nifty is a joint holding of National Stock Exchange ( NSE ) and India Index Services and Products Limited ( IISL ) and Nifty accounts for 70% of total market capitalization.