Cooking vegetables quickly in boiling water to bring out both their flavour and bright colours is called as blanching. But sometimes because of lack of knowledge and improper cooking processes the vegetables after blanching turn brown.
The most likely reason the vegetables turn brown is because we cover the pot with a lid after adding the vegetables. This happens because as the vegetables hit the boiling water, volatile acids are released into the water and are carried away in the steam. When the pot is covered, the steam and the acids that the pot contains are forced back into the water. Once there, the acids react with the chlorophyll in the vegetables, turning them an unsightly shade of brown.
A similar reaction will take place if there's too little water in the pot or if you overcook the vegetables thus prolonging the exposure time to the acids.
So to avoid this, use large amount of boiling water for blanching, test the vegetables frequently to check their doneness, and leave the pot uncovered. Also keep the a bowl of ice water ready as soon as the vegetables are blanched put them in the ice water to cut down the carryover cooking. This is called refreshing vegetables.