Turns out that this was my PhD thesis subject.

To put it simply two-level systems (TLS) are groups of atoms in a disordered solid that present two stable configurations, that is two physical states of similar potential energy separated by a small energy barrier. The barriers need to be small for it to be overcome by thermal fluctuation alone and thus for the TLS to resonate at a frequency close to the frequency of interest.

If you are interested by what exactly are these TLSs at the atomic level, have a look at this paper: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.97.014201

Wonder if it's similar to oscillators[1] in Game of Life. I.e. a some molecules have two different arrangements with same energy, so they can swap between them by absorbing a bit of thermal energy or something.

[1]: https://www.conwaylife.com/wiki/Toad

There's a linked article about the hunt for ideal glass that includes some details about 'two-level systems'. [1]

[1] https://www.quantamagazine.org/ideal-glass-would-explain-why...