Iodine is used to build thyroid hormones, which are essential for mammalian life.[1]
It's one of the most important nutrients for the brain, and deficiency can lead to an estimated loss of 13.5 IQ points.[2] The neurological [consequences] of iodine deficiency are mediated by thyroid hormone deficiency, varying from minimal brain function to a syndrome of severe intellectual disability.[3]
The production of myelin requires Thyroid Hormone, which requires Iodine.[4] Myelin is a covering on the axons of brain cells which increases the transmission signal speed.[5] Myelin is essentially like the insulation covering a wire.
Iodine is also anti-microbial, and is artificially added to milk to reduce risk of contamination.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3649107/
[2] https://www.ncbi.nlm.nih.gov/books/NBK285556/
[3] https://pubmed.ncbi.nlm.nih.gov/15107513/
[4] https://pubmed.ncbi.nlm.nih.gov/10649292/
[5] https://www.ncbi.nlm.nih.gov/books/NBK10921/