The pitchers on your plant are turning brown because the water is not flowing into them. This could be because:
You don't have enough water. Check that the reservoir is full. If your plant is growing in a pot, check that it has plenty of water. The plant needs to be watered more often than usual. Check the instructions that came with it.
The plant's environment isn't right. It might be growing in the wrong conditions. If you think the problem is something else, tell us what you think and someone may be able to help.