The term "residual" is also used in flight dynamics when computing an orbit from observations, e.g., range and range rate (Doppler) from a radar or transponder, view angles from a telescope or antenna, etc.
Because of noise and other impairments, a given set of orbital elements is unlikely to exactly match every single observation so the computer looks for the best "least-squares" fit. That is, it finds the orbital elements that minimizes the sum of the squares of the differences between the modeled and measured values for each observation. A little over two hundred years ago, Carl Friedrich Gauss proved that this gives the most likely values when the measurement errors are all independent and noise-like.
These differences are known as "residuals", and when you hear a FIDO say an orbit is "converging" he means the computer has found a trajectory with acceptably low residuals. When you hear "guidance is converging" (e.g., during a launch) it means the guidance system has managed to get the rocket where it wants to be at a given time, with low residual errors.
Because residuals summarize how well an entire tracking or guidance system is operating you will often see them plotted in mission reports. Ideally they should appear noise-like, so if you see skews or other non-random patterns it's a strong clue that there's an error or failure somewhere that needs to be fixed (e.g., wrong coordinates for a tracking station) or that your model is insufficient, e.g., it doesn't account for all the significant forces acting on your spacecraft.
