In the US, in most states, 'at will' employment often means zero notice is required from either side. A contract can specify otherwise, as can other things (such as a company HR procedure).
> You can't just say "i'm giving you 1 month of formal notice of resignation" and expect the company to be bound to that month... otherwise, to take it to extremes, what's stopping you from giving them a 20years formal notice of resignation?
You actually can say that if you want.
What stops 20 years notice from having any effect is that the company can terminate you anyway in the normal way before that. I.e. they can still make you redundant, fire you, assess your performance etc in all of the usual ways, or in 'at will' locations just let you go without a reason. They will still be subject to discrimination law etc if they fail to comply with all the usual constraints on terminating employments, but nothing about your 20 year notice prevents them from following the normal rules at any time.
ps. I really meant to say "giving 1 month formal notice in accordance with my contract of employment", but I realised in the US people don't always have any notice in their contract (due to 'at will') so I removed the part about being in accordance with it.
Ignore employment as a special case for a moment. In general, for any contract (implied or not), parties can give each other advance notice of something that is going to take effect in future, as if they told the other party on the future date of the effect; the effect will not occur until that date. The other party in the contract can't just decide the effect has taken place earlier. You can also give conditions. In a sense, notice of this kind is just a courtesy, an advance warning if you like.
I believe in US 'at will' terms, Timnit effectively gave notice that she was going to resign at a specified future date under certain conditions. Timing had not actually resigned at the point at which Google is said to have terminated the employment. That makes it a termination.