Figured bass (or Thoroughbass) refers to a shorthand system to designate the intervals to be played above the bass.
Depending on the number of voices, we choose different notes to add:
The following example shows a series of 8/5/3 chords labeled without abbreviations:
The same progression with abbreviated figured bass would include no numbers in the figures:
Consider the following progression and the generic interval labels (unabbreviated figures):
Both 6/3 and 8/6 would be abbreviated to 6. Again, 8/3 and 5/3 would remain without figures (or could include 3 to show that we only have the 3rd and no 5th).
Accidentals next to figures alter those figures as they would on the staff. A line through a figure or a + sign raise it.
An accidental without any number always means altering the 3rd from the bass:
Practice these exercises here