Loot and Spells can only be equipped (placing the card on or around your Hero Mat) when you are resolving a ‘discover’ effect () or a ‘pick up’ effect ().
On the other hand, you can always discard a card from your mat as a Free Action on your turn, placing it into its appropriate discard row. You cannot give a card directly to another hero.
Equipping loot will cover one of the starting items or abilities listed on the bottom of the Hero mat; discarding that loot allows that item/ability underneath to be available for use again. Note that there are limits to how many Loot and Spell Cards you can have on your Hero Mat at one time: