Having an empty soul shows a trait was extracted by force or used too much magic and/or power.
Whenever someone's soul becomes an empty soul, their soul only contains its outline without containing anything in its center. The color of the outline depends upon the trait of the human (as seen in the picture).
What Camila Cuevas Said About Empty Souls
They can be the result of the subject overusing their magic or by someone else extracting the subject's soul's magic by force.
Having this soul means you still have your trait and your magic, but the ability to use your magic is disabled. For example, if Frisk's soul is empty, that means he has his DETERMINATION trait and he has his magic, but he doesn't have enough DETERMINATION in his soul to fight because his soul is empty.
When Chara's soul became empty, they gave it to Asriel to use as a vessel to hold both Asriel's soul and the human souls. Thus, empty souls can be used as vessels for other souls.
When Frisk's DETERMINATION got extracted by Chara in *Determination, they were too weak to fight for the rest of the episode and for the majority of "Your Best Friend." However, their DETERMINATION came back in Your Best Friend when they realized Chara would kill Asriel if he didn't will his DETERMINATION to come back.
The difference between an empty soul and a grey soul is that Empty souls still have their trait, but cannot use their magic. This is vice-versa for grey souls. Cami Post