Accidentals are shown beside notes to indicate their pitch, both when notated on a staff and written out in text. In music based in Western tonality, they usually show that the pitch of a note has been altered so that it does not conform to the prevailing key signature.
In Dorico Pro, each note has its own fixed pitch that is independent of the prevailing key signature, and accidentals are automatically hidden and shown as appropriate. For example, if you input F♮s and then add a D major key signature before them, they do not turn into F♯s; they remain F♮s and show natural accidentals. However, if you input the D major key signature first, any Fs you then input without stating an accidental are input as F♯s.
There are different conventions for accidental duration rules, such as not repeating the same accidental on subsequent notes of the same pitch in the same bar. In music that has no key signatures, some or all notes might require accidentals, depending on the notation convention in use.
You can use accidental duration rules to determine when accidentals are shown, and control how accidentals are arranged in complex chords.