Splice is the ability of some cards to be added onto arcane spells for a mana cost without using up the card. The card your splice ‘from’ is revealed from your hand but doesn’t go into the graveyard, its effect is simply added to the other card.

A nice simple example of splicing is:

Cast Lava Spike cost R for 3 damage to the player and splice Glacial Ray onto it for 1R , and do another 2 damage to the player or other creature (spliced can be retargeted) AND you get to re-use the Glacial Ray for another round (just the Lava Spike goes into the graveyard).