Delve is an alternative cost payment keyword ability. It was introduced in Future Sight. At the time, it was only printed on three timeshifted cards and was a cost reduction. It was re-introduced as the clan specific mechanic for the Sultai Brood in Khans of Tarkir  and Fate Reforged.
From the Comprehensive Rules (Archenemy: Nicol Bolas (June 5, 2017))
- 702.65. Delve
- 702.65a Delve is a static ability that functions while the spell with delve is on the stack. “Delve” means “For each generic mana in this spell’s total cost, you may exile a card from your graveyard rather than pay that mana.”
- 702.65b The delve ability isn’t an additional or alternative cost and applies only after the total cost of the spell with delve is determined.
- 702.65c Multiple instances of delve on the same spell are redundant.
From the glossary of the Comprehensive Rules (Archenemy: Nicol Bolas (June 5, 2017))
- A keyword ability that lets you exile cards from your graveyard rather than pay generic mana to cast a spell. See rule 702.65, “Delve.”
- The rules for delve have changed slightly since it was last in an expansion. Previously, delve reduced the cost to cast a spell. Under the current rules, you exile cards from your graveyard at the same time you pay the spell’s cost. Exiling a card this way is simply another way to pay that cost. [This is similar to the change made to convoke for the Magic 2015 Core Set.]
- Delve doesn’t change a spell’s mana cost or converted mana cost. For example, Dead Drop’s converted mana cost is 10 even if you exiled three cards to cast it.
- You can’t exile cards to pay for the colored mana requirements of a spell with delve.
- You can’t exile more cards than the generic mana requirement of a spell with delve. For example, you can’t exile more than nine cards from your graveyard to cast Dead Drop.
- Because delve isn’t an alternative cost, it can be used in conjunction with alternative costs.
- Death Rattle -
Delve (You may exile any number of cards from your graveyard as you cast this spell. It costs less to cast for each card exiled this way.)
Destroy target nongreen creature. It can't be regenerated.