The Swastika is an equilateral cross with its arms bent at right angles, in either right-facing (卐) form or left-facing (卍). Swastik is an ancient symbol which is found worldwide, but it is especially common in India. Lets first start with its Indian association. The auspicious symbol of the Swastika is very commonly used in Hindu art, architecture. It is usually a major part of the decoration for festivals and special ceremonies like weddings.It can be seen on temples, houses, doorways, clothing, cars, rangoli patterns and also used for meditation.
The Swastik or Swastika's Indian name comes from the Sanskrit word svasti, meaning good fortune, luck and well being. Thus, the literal meaning of the term Swastika would be 'let good-prevail'.
WHAT DOES IT SIGNIFY ??                                                         
Throughout human history the symbol of Swastika symbolises many different things — luck, Surya (the sun), Brahma, or the Hindu concept of samsara.
The swastika is also believed to be one of the 108 symbols of Hindu deity Vishnu and represents the Sun's rays, upon which life depends. It is also seen as pointing in all four directions (north, east, south and west) and thus signifies grounded stability. Some Indians also think that the center of the Swastik represents the uterus, the origin point of the Universe (the vertical line-Shiva and the horizontal line - the female organ). Their cross forms the origin and evolution of the whole world. It also explains the Big-Bang theory of energy flowing into all directions from the origin point in center. 
RIGHT AND LEFT HANDED SWASTIK      
Both the Swastik represent different things. In India the right handed Swastik is a symbol of good energy and is considered very auspicious whereas in Buddhism the left handed Swastik is treated as a sign of good fortune. This left handed Swastik is often seen on the statue of Buddha's chest or foot.  It is also the first of the 65 auspicious symbols on the footprint of the Buddha. This form of the swastika is often found on Chinese food packaging to signify that the product is vegetarian and can be consumed by strict Buddhists. Left handed Swastika is often sewn into the collars of Chinese children's clothing to protect them from evil spirits. In India the left-hand Swastika (called a sauvastika) usually represents the terrifying goddess Kali, night and magic.

     However, this form of the swastik was adopted as the Nazi symbol and lateron went on to be a part of Hitler's party flag.He wanted a symbol like no other, to be unique and one-of-a-kind. He wanted it to stand out and make people fear him. Hitler decided to reverse the design, making the swastika counter-clockwise, symbolizing evil and black magic