A Speed Shrine is a terrain feature found on a few Fields of Justice that grants a moderate movement speed buff to certain champions as they walk over them. The champions that are specifically affected by the buff are dependent upon the map the shrine is located.
Two maps in League of Legends possess speed shrines; the Crystal Scar has three or four, and Summoner's Rift may have up to two at once. The Twisted Treeline does not possess a speed shrine, but the Ghost Relic located at its center can functionally act as one for a single champion.
On Summoner's Rift, killing the Rift Scuttler spawns a team-aligned shrine outside the enclave of the Dragon or Baron Nashor, depending on which one is killed. The shrine offers a movement speed boost of 30% for 1.5 seconds to all allied champions that pass over it, and also grants sight over the speed shrine's area to the killer's team as well.
The shrine is not permanent, only lasting for 75 seconds, but proffers a significant advantage to any allied team that owns one, particularly when attempting to contest the nearby boss monsters. It can also function as a ward that provides irremovable vision over the river to give added safety for a nearby lane.
Unlike on Summoner's Rift, the speed shrines on the Crystal Scar are perpetual, buffing any champion that passes over them regardless of team alignment with a 30% movement speed boost that decays over 10 seconds (12 seconds with Runic Affinity). Their locations are placed such that their use can equalize travel time between any two capture points, whether a champion is moving from the Boneyard in the bottom left to the Refinery in the upper right, or just across to an adjacent point.
Speed shrines allow players to have significantly more strategic options whether they are confronted with a stalemate, or are simply looking to keep an opponent on their toes by launching a timed attack at a cross-map objective.