As Wikipedia quotes, a salute is a gesture of respect and trust among soldiers which encourages a pride in their ever-shining uniforms while at the same time elevates them in their own eyes by reminding them all of that is implied by the profession and its traditions of chivalry and courtesy.
The custom of saluting has evolved gradually to come to be what it is today. It is believed that it began in the late Roman times when a citizen who wanted to meet a public official had to raise his hand in order to show that he had no concealed weapon in his palm. This however grew into a means to show respect.
As you might be aware, our saluting customs are directly descended from the British saluting customs which explains why our Armed forces salute but the question remains, why differently?
In Indian Army, a salute is executed by an open palm gesture with fingers and thumb together and the middle finger almost touching the hatband or the eyebrow. It not only instills trust among the personnel but also proves that the person saluting has no bad intentions and no weapons hidden up anywhere.
Indian Air Force
In March 2006, Indian Air Force issued a new salute norm to its personnel. This new salute involves the palm at a 45-degree angle to the ground and the right arm being sharply raised from the front by the shortest possible way. It is a mid-way between the Army and Navy salute and was standardised to make it more convenient for the IAF. Earlier, IAF hand salute was just like the Army one. Even, the air warriors are supposed to salute without any cap or headgear.
Earlier, sailing ships used tar/charcoal pitch to seal the wood hull from seawater and to keep the ropes from decaying. To protect hands, the officers started wearing gloves. However, the gloves too, used to turn very dirty. In order to not show the dirty palm of their gloves, the officers started saluting with their palms downwards. Now-a-days tar/charcoal pitch disappeared, but still the hands of sailors/officers get dirty due to oil or grease stains while working on the ship. Thus the salute in Indian Navy is executed with the palm facing the ground at a 90 degree angle to the forehead.