cut -d, -f3 extracts the third comma-separated field. It is fast, and it is wrong for any CSV where a field might contain the delimiter.
Quoted fields shift every column after them
"Smith, John",42,london has three fields. cut sees four, so field three is 42 rather than london. Only rows containing a quoted comma are affected, so the output is mostly correct — which makes the error far harder to notice than a total failure.
awk has the same limitation
awk -F, splits identically and shares the problem. Neither tool tracks quoting state, because neither is a CSV parser.
When each choice is right
For genuinely simple data — tab-separated, or comma-separated values that provably contain no commas — cut is correct and fastest. For anything untrusted, use a real parser: csvcut from csvkit, or a library in whichever language is to hand. The cost of the parser is a fraction of the cost of discovering misaligned columns three steps downstream.
Try it: Split by Delimiter / Extract Column on SeoWolf's Notepad.