Akshaya Tritiya is considered to be one of the most auspicious day in Hindu religion. As gold is considered to be a sign of purity and prosperity it is believed that buying gold on Akshaya Tritiya brings good luck, wealth and prosperity to you and your family.
As per Hindu mythology it is believed that Sat-yug began on Akshaya Tritiya and sun shines the brightest on the day. Sat-yug is also considered to be the golden age among all four yugs. It is said that on this very day Lord Krishna handed over Draupadi a utensil which provided a never ending supply of food for Pandavas during their exile period.
Akshaya Tritiya also holds great importance in Jain community and it is an auspicious day for them as well; being associated with Lord Adinatha (Rishabhadeva) who was first of their twenty four Tirthankaras.
Apart from religious belief there's no such specific reason on why you should buy gold only on Akshaya Tritiya or on any other auspiciuos day. In-fact over the years it is been observed that gold rate increases a bit on Akshaya Tritiya than its previous day as excess buying creates a strong demand which pushed the gold rate northwards.
Also, check for historical data of gold rate on Akshaya Tritiya in the past few years.