If the roll of the dice + appropriate modifiers meets the DC, it is counted as a success. I always remember, "meets it, beats it". :)
So in terms of this, your spell save DC is what they have to beat. That is calculated at 8 + proficiency bonus + spellcasting mod (charisma for a bard). The highest this can be is 19 (8 + 6[prof] + 5[cha]).
The save is a constitution save, so your target must roll a d20 and add their con modifier to that. If their roll + modifier is the same or higher than your spell save DC, then the spell has been surpassed and the effects do not work.
For some spells, like fireball, the save is only for half damage. So if the target fails the save, they would take the full damage, but on a successful save (they beat your spell save DC) they would take half damage. In terms of blindness/deafness, your spell would have no effect if they succeeded your save.