Immunity against a condition would simply mean that if this condition were to affect it, it would not do anything instead.
Each creature in a 30-foot cone must make a saving save of Wisdom or drop what it holds and become scared for the duration.
The target always makes a saving throw as expected, but it can not be scared, that it fails or passes. Any modification made by an omen or by Cutting Words would be lost if the characters were not aware of the immunity.
Another example would be a magician casting Sunburst on an ocher jelly.
In case of failure of a save, a creature takes 12d6 damage from radiation and is blinded for 1 minute.
An ocher jelly is immune to the Blind condition, but a saving throw is still needed.
The undead and seepage have a disadvantage on this saving throw.
The ocher jelly actually makes the saving throw with a disadvantage, but it still can not be affected by the effect of blindness of the spell.
If a paladin throws the thunderclap on the same ocher jelly;
In addition, if the target is a creature, it must make a successful force save roll or be pushed about 10 feet from you and hit on the belly.
Ocher jelly is not affected by the spell, but a saving throw is still needed as it can be pushed.