After finding formal definitions in various texts (see, eg, Witten, _Notes On Some Entanglement Properties Of Quantum Field Theory_, Rev. Mod. Phys. 90, 45003 (2018), doi:[10.1103/RevModPhys.90.045003](https://doi.org/10.1103/RevModPhys.90.045003) arXiv:[1803.04993][1]), I have ($\text I$) not been able to obtain a good intuition for them and ($\text{II}_1$) have not seen anyone relate such factors to more commonly understood Hilbert spaces such as $L^2(\mathbb R)$. This is very likely for good reason, but it would be nice to have these ideas come down from the clouds so that one can present them to non-mathematicians and (maybe this is too ambitious) laypeople.

Some more technical sources which helped me answer this are [here][2] and [here][3].


  [1]: https://arxiv.org/abs/1803.04993
  [2]: https://mathoverflow.net/questions/371383/what-is-a-type-textii-1-factor-von-neumann-algebra
  [3]: https://www.math.ku.dk/english/research/conferences/what_is/a_II_1_factor.pdf