Administered prices are prices set by the government or an organization instead of the usual supply and demand forces.
Let's say you want to buy a toy from a store. If there are a lot of toys and not many people want them, the store might sell them for lower prices to make sure people buy them. But if a lot of people want the toys and there aren't many in the store, the store might raise the prices so they can make more money.
However, sometimes the government or an organization might say, "We want to make sure that people can afford this toy no matter what." They might set a price that the store has to sell the toy for, even if they would normally sell it for a higher price.
The same thing might happen with things like gas or electric bills. If the government thinks that the prices are getting too high, they might step in and say, "You can't charge people more than this."
This helps make sure that everyone can afford basic necessities, but it also means that the price isn't based on things like how much it costs to produce the product, or how many people want to buy it.