Braces themselves do not damage the teeth, but they create conditions that can increase the risk of decay if oral hygiene is not good enough. Because of their shape, braces trap bits of food, and if they are not cleaned regularly, the plaque that builds up can attack the enamel, especially around the base of each bracket. The first stage of enamel damage, known as demineralisation, shows up as white spots, which can spread over a larger area with time. If action is taken at the first signs of this process, the damage can be stopped and even reversed.
To avoid this risk, you need to make an effort to keep up good oral hygiene. Foods high in sugar, such as chocolate and biscuits, and acidic drinks such as fizzy drinks and fruit juices, make decay more likely and should be limited. At every check-up, the orthodontist checks the condition of your teeth and gives advice on improving your hygiene, but keeping it up is also down to you.
This answer is for general information. Your own case needs an examination by an orthodontist.