Subwoofer advice sought

I have a pair of Totem Forest Signature driven by a 100 wpc Unison Research Due amplifier. It has loads of power to power these speakers and has a subwoofer output. I have a medium sized room.

My local hi fi dealer said I would get better sound with the addition of a subwoofer with the results being better midrange and sound staging as well as better bass.  How is this possible?

The 2 subwoofers I am looking at are the Totem Storm and The REL T/7i. My dealer sells the REL and says it  would be a good match for the Totem speakers as it is very quick and tuneful.  Can anyone explain why a subwoofer would make these differences to the sound?  I also would be interested to hear from anyone with experience with these specific subwoofers or pairing a subwoofer with Totem Forests. Thanks.