A lot of organic molecules, including DNA base pairs, have a property called "chirality" (aka "handedness") where the mirror image of a molecule cannot be superimposed on the molecule itself (like hands).

DNA is used as a template for creating proteins. All living organisms have "right-handed" DNA, so all of our proteins also have the same handedness. The "mirror life" they're talking about would be organisms with "left-handed" DNA and proteins.

A molecule's chirality has a ton of impact on its chemical properties. For example, the decongestant in an over-the-counter nasal spray is l-methamphetamine; its right-handed version, d-methamphetamine is — you guessed it — meth.

Proteins are incredibly large and complicated molecules that have intricate 3D structures. Interactions between different proteins depend on this 3D structure — for example, that's why there's been so much concern in minor changes in the COVID "spike protein" that allows it to enter cells and get detected by the immune system. That's not even to mention the danger posed by misfolded proteins (which can caused diseases like alzheimers) or prions (which cause diseases like mad cow).

The concern is that: living organisms are literally not set up to handle reverse-handed proteins. Hypothetical "mirror bacteria" made out of reverse-handed DNA, proteins, etc have the potential to easily cause ecological disaster.