Cautionary accidentals are those little friendly reminders that the note you are looking at (about to play) is actually different than the same note previously. Sometimes this is because we've crossed a bar line and the altered note in the previous bar is no long altered, but should be played in the appropriate key signature. Othertimes notes an octave different from the altered note are played in a bar after the altered note, but these notes of a different octave don't retain the alteration (like they would if they were in the same octave). And then there are those times when the key signature has changed and a friendly reminder is presented the first time a note is played in the new key - just to remind the player "you're in a new key."
When I was playing fairly regularly, I didn't find it all that necessary to have cautionary accidentals in the part because the rule is, if the note is altered, either flat or sharp, than that note retains that alteration until the next bar. Notes of the same pitch but different octaves are not altered unless specifically specified. As such, I typically just kept that in mind when playing. The occasions where an altered note is followed in the next bar by the same note unaltered are rare - or so I thought.
One of the comments made about the symphony during the rehearsals was the lack of cautionary accidentals. I didn't bother putting them in the parts or the score. Well, this created more than a few interesting tuning events and a far number of clarifications during rehearsals (not all of them were clarified correctly, I might add). So, I decided I needed to go through the score and put in the cautionary accidentals to the score (I'm going through the score to correct a few other incidentals, so why not add this correction to the list)
To my shock, there are over 30,000 cautionary accidentals needed in the score. The symphony, which is 5 movements for a total of 50 minutes of music, is obviously a lot more chromatic than I first thought.