Salt Damage

It appears to be the result of salt damage to your Spathiphyllum. This is quite common in house plants. The salts accumulate in the soil because they are not being leached out properly when watering. If possible, about every month or two, give your plant a nice shower using room temperature water. Let the water flow through the pot and out the drainage holes in the bottom. When watering in between showers, if possible, water in a sink or outside until the water comes out the drainage holes in the bottom. Try not to let it sit in the drained water. If you fertilize, do so lightly as this is another source of salts in the soil. Here is a link that might be helpful:
http://coopext.colostate.edu/4dmg/Plants/guidline.htm#Signs of dehydration and overwatering