What happens to Neo twice in a row that clues Trinity about a glitch in the system in the movie "The Matrix"?

In "The Matrix" (1999), when inside the program simulation, Neo (Keanu Reeves) experiences déjà vu when a black cat passes him twice. The actions of the cat clue Trinity about a glitch in the matrix system.

The momentous scene in the movie occurs when Neo witnesses a black cat replicate exact behavioral twitches twice down a hallway, making him say, “Whoa. Déjà vu.” At that particular juncture, the film opens up a seminal plot propeller and allows the audience a glimpse into the concept of “a glitch in the matrix.” The event makes it clear that the great programming saga, using the matrix as an experiential reality that has a tangible impact on humans and machines alike, isn't totally 100 percent perfect. The déjà vu cat acts as a signifier that the matrix's code has changed in some way, which is not necessarily for the best.