There are three different kinds of Jewels to collect; Goddess, Kappa, and Truth. After you collect 9 of each kind, they'll combine into the full Gems. The Gems can be used just like one of your tools and you can regain your strength and fatigue if you use them. The Truth jewels will only appear after you have obtained the cabinet from the Tv Shopping show. The Goddess and Kappa jewels can be found hidden inside of rocks in the mines.
Gem of the Goddess
Regains your Strength if equipped
Spring Mine, floor 60
Gem of the Kappa
Regains your Fatigue if equipped
Lake Mine, floor 0
Gem of Truth
Displays your Fatigue and Strength
On your dog house roof
The Kappa and Goddess Gems are handy because they'll regain all of your strength and fatigue. Spending time in the Hot Springs or using your bathroom won't recharge you fully, but using the two gems will. If you want to see how weak you are, equip the Truth Gem and then look at it in your inventory. It will tell you how many points you have left in strength, and how many more points you need before you pass out from fatigue.
The Truth Gem doesn't actually do anything else other then display the point values of your strength and fatigue. If you want to regain your strength and fatigue, you have to equip the Kappa and Goddess Gems one at a time, then check to see how far you are by equipping the Truth Gem. The Gems also only regain their values if you're outside where time can move.