Training Grounds is a fascinating little enchantment that makes a creature’s activated abilities considerably cheaper. It actually saw some competitive play back when Extended was a viable format, combo-ing with Izzet Guildmage to make its 3 converted mana cost abilities only cost one red and one blue. The combo also involved Manamorphose, which allows for essentially infinite card draw and mana. This could still be a viable combo in Modern, so it will be interesting to see if we ever see that sort of Storm deck again.
The most popular use of Training Grounds in Commander is in Sliver Overlord decks. This is because the Overlord has two 3 mana abilities - one which adds a Sliver from your deck to your hand and the other which lets you gain control of target Sliver! Training Grounds makes each of these abilities cost only a single mana. It also makes Sliver Queen's 2-mana Sliver token creation ability only 1 mana, as well.
Tasigur, the Golden Fang and most recently The Scarab God also take advantage of Training Grounds, seeing their own activated abilities cost half as much. This is an Enchantment that gets better with every good creature with activated abilities that gets printed. It's become nearly $20 a copy for a reason and should see a reprint in a Commander-related product one day.