Yes, it's basically part of a low pass L-C (or R-C for high frequencies) filter for the analog Vdd on the chip (with C9). Ferrite beads act like very low resistance (< 1 Ohm) for DC, inductors (several uH) for low RF frequencies and they act like resistors (hundreds of ohms to 1K or more) for frequencies in the 100MHz range.
Ferrite beads are normally specified in ohms in the resistive region (relatively high frequency- usually 100MHz) where they are very lossy, but they have an inductive region at lower frequencies. Note that care must be taken with this kind of circuit that noise inherent in the supply does not resonate at high Q with the ferrite and capacitor or the bead may actually result in more noise on the power rail. A good reference on beads can be found here. This sort of thing can cause all kinds of grief if the SMPS noise is (or has a harmonic) close to resonance and it changes with loading or input voltage or temperature to move in and out of resonance.
If you simply omit it the chip will not work properly since there will be no power supplied to Avcc. If you replace it with a short, the chip will operate normally, however you may see somewhat higher noise on ADC readings and possibly other subtle effects on analog performance.
R33 may have been a thought to allow for a ferrite bead in the analog ground (usually not a good idea) or it may be used as a net tie to enforce a single point connection between the analog ground nets and the ground.
Given your level of experience, I suggest you focus on making a single low impedance ground. Separate analog and digital grounds never benefit digital circuitry. If they are not done correctly, they also do not benefit analog circuitry. So just ground everything together (no separate analog and digital ground). Use boards with continuous solid ground planes. You can also make an artificial GND plane on a single layer board using copper tape.
If you have to run wires from board to board, make half of the wires GND. In other words, for every signal that goes from board to board, there should also be a ground wire. For every power connection that goes from board to board, there should also be a ground wire. Twist each power or signal wire with its dedicated GND. This will save you a lot of trouble.
Each board should have room for a large bulk capacitor of at least 220 uF. This is in addition to the 0.1 uF per power pin and/or whatever is recommended by the chip vendor.
Order a kit of cable ferrites so that you have it ready just in case you have unexpected noise problems. The board-to-board wires can be routed through the ferrites to suppress high frequency noise.
In the schematic, place small resistors in series and small capacitors to ground on the analog inputs coming back from the reflectance array. Basically you want to be able to make an RC low-pass filter at each input. On the layout, place these RC components close to the actual analog input. Make sure you have an array of different resistor and capacitor values on-hand so you can tune the cutoff frequency of the RC filter.
Good luck! Have fun.
Best Answer
Digital circuits are noisy, but they can (mostly) handle their own noise without noticing. Analog circuits notice noise a lot; in fact, they have to pass noise just like a signal because they really can't tell the difference.
The best way to keep digital noise out of analog circuits is to keep them separate, both physically and electrically. But they have to be connected somehow in order to convert from one to the other, hence the jumper in exactly one spot, which is probably next to the converter on the physical board.