I view a 'gambit' as taking a gamble (sometimes a HUGE one).
The farmer's gambit is basically building nothing but granaries, workers, and settlers. If nobody attacks you, you expand very well, because you devoted 100% of your resources to expansion. If somebody does sneak-attack you, the game would probably be over for you.
A good example of the farmer's gambit in action can be seen in the screenshot of this post:
http://forums.civfanatics.com/showthread.php?postid=1088338#post1088338
There is also the warrior's gambit, which is sending your first two warriors directly at your neighbor's capital in hopes of defeating their lone defender. This works best before they have Bronze Working (so they won't have spearman), and this is usually done ~3000 BC (sometimes earlier).
If you win, you already defeated a civ, and captured a city. If you lose, you face the wrath of the AI counter-attack.....
Don't ever try this on anything above Monarch.
NewDestroyer- You don't want to pop-rush settlers or workers. Rushing them with cash (when you get out of despotism) is a better idea.
But anyways- To poprush a settler, I would only suggest it in a population 4 city that is 95% corrupt (only producing 1 shield/turn), but even then you have happiness problems to worry about. If rushing a settler, wait until the city has built up 10 shields, so when you pop-rush, the citizen gives you 20 shields, which will give you the 30 shields you need, plus still have the population points to be able to send 2 citizens out of the city (the settler).
You'd be better off building workers non-stop in those super-corrupt cities.