The red dot is called a bindi. It is a form of body decoration. Culturally, hindus attach a lot of importance to this ornamental mark and call it by various names - pottu, bindi, tikka, tilakam and sindoor. There are various theories on why it is important and I will share a few here.
why should a girl put a bindhi as per tradition
The 'Hot' Spot - The area between the eyebrows on the forehead is the spot of 'agna' chakra. In yogic science, this spot is considered as one of immense power, often called as the third eye.
The 'Magic' Ingredient - Traditionally kumkum ( a mixture of turmeric and lime) or chandan (sandalwood) was used to mark a bindi. Kumkum is hygroscopic in nature and can greatly assist to remove excess water from one's head. Tumeric's anti-bacterial properties are helpful too.
Further, the colour red is believed to aid spiritually. Chandan or sandalwood is renowned for its 'cooling' properties. For a hot tropic country, application of chandan on forehead ( a nerve centre) helps to cool one's entire system.
On a religious note, the color red symoblises 'shakti', the goddess of strength. A kumkum is marked on girls after marriage denoting strength and wishing for peace.