The picture of our boss won the special prize at the contest!
Here are the specially selected cosplayers.
I heard that Koichi eats the best, specially selected black garlic before going to bed every night.
If something is special you choose it. That makes it a special selection of yours and it gets a special prize that only you could give!
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.