A penguin's moult is sometimes called a catastrophic moult, because unlike most birds that will moult a few feathers at a time, penguins moult all of their feathers all at once. If you look at some of these pictures you can see that catastrophic is a good description, they often look like exploding pillows.
Moulting is a 3 stage process and starts weeks before the penguins actually replaces any feathers. Their bodies are making the new feathers while they are gorging themselves on fish which they must do to increase body weight to endure the 2nd stage. Penguins are not waterproof when they moult, so in stage 2 they stay on land for 2-3 weeks fasting until the new feathers have emerged from below the skin. When the weather is hot the keeper team apply factor 50 suncream to their bare skin as sometimes in captivity our penguins lose their feathers and look patchy and bare before the new feathers are ready to push through. During that time they will not eat, so a few weeks prior to the moult they will increase their food intake to build up a fat reserve to live off of while they are on land. Since we record how many fish each penguin eats everyday we can usually recognize when a penguin is getting ready to moult since their daily food totals can double or even triple. In the wild stage 3 involves returning to the sea to replenish lost body weight.
Here are a few pictures of some of our penguins right before they start moulting, notice how much bigger they look than a normal penguin.