There is no "mystery" - we just don't understand it and to truly understand requires a very open mind and "shraddha" - faith!
How much "power" you ascribe to a symbol depends upon how much you value you have for what the symbol stands for.
Sri yantra is a symbol. It also symbolizes a journey from our mundane world to attaining the Goddess who resides in the middle of that symbol, going through many steps in a methodical fashion.
Several chapters of Lalitha Sahasranamam, Trishathi, etc are dedicated to descriptions of the Sri yantra and regulations about its worship. (Not a bad summary at Wikipedia Lalita Sahasranama) Here is a high-level overview, that I learnt mostly from the amazing discourse on Soundarya Lahari by Kanchi Paramacharya in Deivathin Kural
We have to understand Devi upasana through 2 perspectives - a symbolic and mental . During early stages of worship, we use "external" symbols and methods but over time, can evolve to more of a "mental" approach. An analogy is that of a child learning to add using his fingers, but later not needing his fingers to add and able to do it mentally.
Sri yantra, at one level, represents the physical abode of Devi (variably called Lalitha, Tripurasundari, Parashakti, Durga, Kameshwari) The above-mentioned works describe Lalitha's abode as a city above the Mount Meru - Sripuram or SriNagaram. It is a kingdom by itself surrounded by concentric walls in the center of which Lalitha rules. Each wall/circle represents some special thing in creation - what is notable is that the walls progress from the grossest to the subtlest. So, the outermost circles are made of gross metals like iron, copper, lead. The walls then start getting subtler.. plants, trees, then to subtler things like words, music, then to emotions like bravery and love and finally culminate in her house - "Chintamani grham" which indicates the highest thought which is of God or Self. (chinta meaning "thought") Inside the "chintamani grham", you see Lalitha Tripurasundari seated in a throne held by other gods (including Sadashiva, Brahma, Vishnu and Rudra), indicating that she is the shakti behind creation and even the creator/protector/dissolver can do nothing without her.
Devotees of Lalitha use a Sri yantra or Sri chakra as a representation of that Sripuram. You can see flat 2D versions or 3D versions also called Meru being used. (pictures at end) As a method of worship, they proceed through each wall through specific prayers until they reach the Chintamani grham and attain the feet of Lalitha. The methods are very specific and thought to bring many siddhis (powers). They are also tied to Kundalini yoga. This is the part that creates the "mystic"/"esoteric" viewpoint - it is believed to give ill effects if not followed properly under the guidance of a proper teacher, just as a wrongly-done hatha yoga pose can cause physical problems. Common people are discouraged from Srividya upasana because most don't have the mental strength and commitment to carry them through.
Now, let's delve into the "mental" perspective. The journey up the Meru, into Sripuram, crossing each wall and finally merging into Her is also a spiritual journey. One slowly loses grip on the world and takes steps towards Her. One discards attachment one-by-one to material possessions, then one's skills, reputation, then one's family and finally even one's ego and thought to finally to hold that one thought of Her.