In the world of Star Wars' Galactic Republic, the Jedi act as peacekeepers, which they achieve in part through their ability to perceive the future. However, in Attack of the Clones, Yoda explains they can no longer see this future due to the shroud of the Dark Side, which has inexplicably affected their powers. This limitation plays directly into the hands of Palpatine, who uses it to start the Clone Wars and turn Anakin Skywalker into Darth Vader.
Though the exact method by which the Sith can cloud the vision of the Jedi is established in the films, it is still vaguely fleshed out. The now non-canon Legends stories provide a more in-depth explanation as to how the prescience of the Light is able to be corrupted by the dark.
Looking at the films first, George Lucas provides a somewhat satisfactory explanation for the way the Dark Side is affecting the Jedi. He writes their vision has been "clouded," making their sight similar to that of someone looking through a fog. For some events, they are completely hidden, and for others, they are vaguely defined. This means the Jedi looking ahead may know nothing or only pieces of the future.
When Anakin discovers his mother has been killed by Tusken Raiders and reacts violently, Yoda perceives this disturbance in the Force. However, he only vaguely understands what occurred and can conclude that something bad has happened to Anakin. Returning to the fog allusion, Yoda can see the general outline of suffering but not what happened exactly. Perhaps if his vision had not been clouded, the Jedi may have been able to address Anakin's underlying emotional issues before Palpatine had a chance to manipulate him.
One important paradigm to understand is that the Force does not appear uniformly throughout the universe, and it often appears in a highly concentrated nexus, an idea that many trace back to the cave on Dagobah where Luke fought what he believed to be Vader in The Empire Strikes Back. In the film, Yoda says, "that [cave] is strong in the dark side of the Force," implying that both people and places can be conduits of the Force.
The expanded universe publications develop this idea further to reveal the underlying methods used by the Sith. In Troy Denning's Tatooine Ghost, the nexus idea is used to explain that the place where Anakin murdered the Tusken Raiders has become a nexus of dark side energy.
In much the same way, James Luceno's Tarkin explains that the Jedi Temple, the Order's headquarters on Coruscant, is built on top of an ancient Sith shrine. This concept was meant to be explored in the Clone Wars animated series, but it was canceled before the arc could air, and it was not picked up again when Disney ordered a final season.
The dark side energy seeping from the shrine would have had some effect on the Jedi's abilities, gradually clouding the purity of the Jedi over millennia unbeknownst to them. However, this does not fully explain why someone like Qui-Gon Jinn, who spends most of his time away from the Temple, would have also been affected. This explanation is given in James Luceno's Darth Plagueis, where the titular character and his apprentice Sidious spend months undergoing a ritual to tip the overall alignment of the Force in the Dark Side's favor.
This deep meditation helps them to "assert their sovereignty" over the Force and make the entire galaxy a sort-of Dark Side nexus. Therefore, regardless of where in the galaxy one is, the clouding effect would continue. Though not directly stated, it is this overpowering influence of the dark side on all living beings that likely causes the trade war between the Naboo and the Trade Federation, influences the Confederacy of Independent Systems to leave the Republic and kick-starts the Clone Wars.
These conflicts have a compounding effect in that they themselves further strengthen the Dark Side. Much like Anakin's violence against the Tusken Raiders increased the power of the dark side in one location, the violence of a galactic conflict creates nexuses on countless planets. This is all part and parcel of Sidious' plan to overthrow the Republic and Jedi to create his Empire.
These ideas play into the overarching theme of the Star Wars franchise, in particular the constant struggle between good and evil. Being negligent to the inherent darkness hiding just beneath the surface, like the Jedi were, can cloud perception and have disastrous results. Keeping the peace, as the Jedi wanted, is a never-ending quest to stay one step ahead of the fomenting storm.