My question is what sample skipping means, and how the digital filter comes into play... does it mean that the sensor, internally, makes ADC conversions at 2400 Hz, applying the filter, and gives you output at 80 Hz, or does it make conversions only at 80 Hz ? And if the latter holds, what is happening to the 40 Hz filter ?

Yes, that's it - the breakpoint of the digital filter is not the sampling rate. The sampling is at 2400Hz, the digital filter then produces filtered samples at 2400Hz. Since there should be no useful information above 40Hz you only need to (resample) this signal at 80Hz to get all the useful data. This does rely on the filter being a brickwall and not letting any appreciable signal through at/above 40Hz (such signals would create aliases below 40Hz). However digital filters can have very large numbers of poles and be very close to an ideal brickwall filter.

If there were no digital filter and you read samples at 80Hz then all the multiples of 80Hz would alias all the other multiples of 80Hz (ie 10, -70, 90, -150, 170, -230, 250, 330 Hz would all alias each other, as would 20/-60/100/-140/180/-220/260/340 etc. This would mean the different frequencies would all pollute each other.

(-70 Hz is like 70Hz but time-reversed, so its 70Hz at a different phase).

In order for no frequency aliasing to take place there should be no frequencies from the sensor at or above 1200Hz to start with (so that sampling at 2400Hz doesn't loose information - this will be done with some crude analog filtering I suspect), then the digital filter removes all signals at or above 40Hz, so we can then safely resample at 80Hz. Technically the term for resampling at a lower rate is called "decimation" (the opposite is interpolation), and a combined low-pass filter and decimation step is usually called a "decimation filter" - a special case of resampling.