Why has the definition of 1 calorie been taken to be the energy required to heat 1 gram of water from 14.5 to 15.5 degree centigrade at standard pressure? Is there any specific reason for taking the temperature from 14.5 to 15.5?
The reason for defining a specific starting point is to remove any doubt of how much energy 1 calorie is. You can just say that it is the energy required to warm 1 gram of water by 1 degree, but that is a different value depending on if you are referring to ice, liquid water, or steam. Even within the same state there are slight differences due to changes in density, etc. as illustrated by the wiki page in the comments. Even worse, the value of 1 calorie could be many times its usual value if you measured it as the amount of energy to raise water from 95.5 degrees Celsius up to 100.5 degrees due to the latent heat of vaporization.
As for why the specific 14.5 starting point was chosen, there may be some historical reason, but there is not function reason beyond just to make sure everyone is actually using the same unit. With all this confusion, it's no surprise that the Joule has become by far the favored unit in modern studies!