Precursor statues are Precursor artifacts featured throughout the Jak and Daxter series. They are multi-functional statues that were built and left behind by the Precursors. Constructed from either Precursor metal or stone, they were designed to resemble different creatures but all with the head and visage resembling the godly mythos the Precursors concocted to encourage worship (an insectoid head, large bug-eyes, and a pronounced proboscis extending from the base of the nose or crown).
There were many different types of Precursor statues seen throughout the game, each serving different purposes. These included oracles (and oracle totems), Precursor robots, Precursor idols, crystal hunt Precursor statues, orb search Precursor statues, and Precursor totems.
While there were various other Precursor-like structures, these statues are specifically able to be interacted with in some capacity as opposed to merely decorative.
Oracles were sacred channels through which the Precursors would communicate with the world's inhabitants, namely Jak. They were placed in set areas, and appeared only in The Precursor Legacy, Jak II, and Jak 3. Most oracles looked the same, with a massive head in proportion to their body, a proboscis with a very wide opening (through which the oracle would dispense different things, like power cells or power-inducing bolts of dark eco), and a compact build with a blue gem in the chest (placed behind the proboscis). The eyes would either be filled with power cells (The Precursor Legacy) or a bright blue energy (Jak II).
In Jak 3, there were three massive oracles placed in the center of the Monk Temple, which appeared to be made of stone rather than Precursor metal, and had a similar-looking face with different details and a non-functional proboscis. Its body was more humanoid in structure, and instead of imbuing dark powers via a bolt of energy, it imbued light powers via a beam from the ceiling seemingly disconnected from the oracle itself.
Technically oracles could take the form of any structure, such as a large bust of Mar from the Tomb of Mar or the oracle totems from Spargus and the Haven City Slums. The term "oracle" is applied to any device through which the Precursors directly communicate with a person, excluding those which repeat pre-recorded messages non-exclusive to chosen people like Jak.
Precursor robots were large, humanoid-shaped battle mechs, often built with on-board weapon systems. Several of these could be seen in various areas in The Precursor Legacy and Jak 3, though only two functional robots were ever observed to be brought back to life. The first belonged to and was operated by Gol Acheron and Maia, who had reconstructed it from parts they scrounged up via lurker labor. It was used in the final boss fight against Jak, but was ultimately blown up, with the head sinking into a large dark eco silo along with the twins.
The second one belonged to Veger, though he did not directly control it. Instead he summoned it, presumably from his staff, and sicced it on Jak and Daxter during the mission "Defeat Veger's Precursor robot", though it too was ultimately defeated (however there were still imprints of two other identical robots which could presumably be similarly revived).
Side mission statues
In The Lost Frontier, there were two kinds of Precursor statues which gave side missions. These included very large, oracle-like statues placed at each hub location, as well as much smaller versions of the same statues barring two arm-like emplacements found on the larger versions.
The large versions assign dark eco crystal hunt missions, wherein Jak has to search for a large amount of dark eco crystals growing along the structures of the surrounding areas, shoot them down, and return the energy back to the statue. The messages given by these statues are pre-recorded and could theoretically be given to anyone, thus they are not considered real oracles.
The second variety are found in Aeropa, Brink Island, and the Brink volcano, and give search missions for Precursor orbs around different spots in the city. They do not give messages like the larger variety but do share an identical model.
Precursor idols, also new to The Lost Frontier, were statues that were capable of imbuing set eco powers into its subjects, namely Jak and one known successful example of an ape known as the hyper mutant.
The first one, which gave the eco amplifier power, was located on Brink Island, on the way to Tym's treehouse during the mission "Look for a way off the island". The next, which gives the eco construct power, is located shortly after in the same location, on the path to fight the Uber-Bot 888 during the mission "Retrieve velonium power pod". The third, which gives the eco rocket jump power, was located prior to the entrance to the actual Brink volcano itself, during the mission "Search volcano for eco seeker".
The fourth, which gives the eco reflexes power, is located in the power station at Far Drop during the mission "Defeat the dark mutants". The fifth, which gives the eco teleport power, is located in the Aeropan research rig during the mission "Search for light eco". The last, which gives the eco shield power, was located outside the Aeropan barracks" during the mission "Search the barracks for seeker piece".
Also new and unique to The Lost Frontier were Precursor totems (not to be confused with the aforementioned oracle totems), which were statues that specifically served to interact with Jak's eco powers. There were two kinds, the first being a round platform with a small Precursor head which would refill Jak's eco power reservoir upon standing on it. While standing on it, the platform would release small particles of every color of eco, which would allow the platform to refill all colors of Jak's eco power.
The second kind of Precursor totem (also known as an idol but not to be confused with "Precursor idol"), is a larger statue with which Jak could swap places via his eco teleport power. These were slightly smaller than the Precursor idols, but looked a slightly different in terms of detail. They had strange, presumably Precurian lettering across their fanned cap.
Behind the scenes
In early versions of The Lost Frontier, it was stated that Precursor idols "awakened" secret powers that Jak already possessed. However this was eventually taken out of the game, and it was later seen that those same powers could be injected into different individuals, namely the hyper mutant. Thus, idols instead impart powers unique to the respective idol.