It's worth noting that each attribute score generally correlates to specific kinds of spell saves.
STR saving throws are forced by spells that require physical strength to resist. For instance, Entangle forces a STR saving throw to determine if those in it's area can prevent the vines created from restraining them by pushing them off of them.
DEX saving throws are forced by spells that require reaction speed to evade. For instance, Fireball forces a DEX saving throw to determine if those in it's area can evade the flames well enough to only take half of the damage from the heat.
CON saving throws are forced by spells that require the ability to endure against its affects. For instance, Cloudkill forces a CON saving throw to determine if those subjected to its poisonous fumes can withstand the effects of the poison well enough to only take half damage.
INT saving throws are generally forced by Illusions such as Phantasmal force. It represents the minds ability to discern reality from the illusion.
WIS saving throws are generally caused by charm spells. Spells such as Geas force a target to make a WIS save to see if the target can resist having the will of the enchanter imposed upon them.
CHA saving throws are few and far between. I don't understand them well enough to give a good explanation as to why you make them.
