Where did the diagram come from - supplied or traced out by you or others?
S1 connections are incorrectly shown - this raises questions about the accuracy of the rest of the circuit. As shown, S1 operating or releasing creates a short break in the supply voltage while the switch transits between states. It is vanishingly unlikely that this is what is intended. It may just be meant to be an in/off SPST but drawn wrong.
Brief: If noise from the motors modulates the LEDs then the illumination of the white-line(s) will vary and the motors will be influenced. Adding capacitors across the LEDs is an attempt to minimise the noise effect on motor drive - quite possibly the need was empirically determined when the system worked worse with them absent.
R13 and R14 are light controlled resistances.
D1 and D5 provide illumination for a white line (possible one each side or two lines or with a middle position shield, and vehicle steering is controlled by varying the illumination of R13 and R14.
ICA1 & B are comparators which are both fed with signals proportional to the illumination of the two sensors BUT with opposite sense.
In an ideal and unachievable state, When the vehicle is running 'straight and true' both sensors are equally illuminated. This state would result in indeterminate comparator switching and the vehicle would "jitter" around the mid point.
When R13 is more illuminated than R14 IC1A-3 will be of lower voltage than IC1A-2, IC1A comparator will be off, IC1A-1 will be low, Q1 will be turned on and M1 (left hand motor) will be powered. Conversely IC1B-7 will be high and motor M2 will not be powered.
When R14 is more illuminated than R13 M2 will operate and M1 will not be powered.
SO - what are the capacitors for?:
The Robot is battery powered and can be expected to produce a significant amount of noise on the supply rail. It will benefit from the addition of significant capacitance on the rail - 100 uF minimum and 1000 uF+ would not go astray.
Steering operation is critically dependant on R13 and R14 providing accurate estimates of the relative illumination of the track that they are monitoring. When running at close to equal, small signal variations in one direction will swing them across the threshold and toggle the motor drive outputs.
If noise from the motors modulates the LEDs then the illumination of the white-line(s) will vary and the motors will be influenced. Adding capacitors across the LEDs is an attempt to minimise the noise effect on motor drive - quite possibly the need was empirically determined when the system worked worse with them absent.
Hysteresis: An improvement in operation (or not) MAY be obtained by providing a small amount of positive feedback to the sensing circuit. Adding two resistors (try 1 MOhm each to start) from IC1-1 to IC1-3, and the other from IC1-7 to IC1-5 will add positive feedback to the comparators. Whether this improves operation is left as an exercise for the student.