MaxW's comment linked to the relevant Wikipedia page:
Nicotine is regarded as a potentially lethal poison.[17] The LD50 of nicotine is 50 mg/kg for rats and 3 mg/kg for mice. 30–60 mg (0.5–1.0 mg/kg) can be a lethal dosage for adult humans.[11][56] However the widely used human LD50 estimate of 0.5–1.0 mg/kg was questioned in a 2013 review, in light of several documented cases of humans surviving much higher doses; the 2013 review suggests that the lower limit causing fatal outcomes is 500–1000 mg of ingested nicotine, corresponding to 6.5–13 mg/kg orally.[13] Nevertheless, nicotine has a relatively high toxicity in comparison to many other alkaloids such as caffeine, which has an LD50of 127 mg/kg when administered to mice.[57]
You ask:
That's pure nicotine and they claim that 2-3 drops of that can kill you. Is that true?
"Drops" is an imprecise non-quantitative term, but let's suppose that a drop is about 20 μL in volume. Then 3 drops is 60 μL or 0.06 mL. The density of the nicotine "oil", if pure, is about the same as water's. So 60 μL should equal about 60 mg of nicotine. According to the paragraph from Wikipedia, this corresponds to a widely used figure for a lethal dose.
However, note the text later in the paragraph that a lethal dose is closer to 500-1000 mg. That would require ten to twenty drops, not just two or three.
Undoubtedly what is a "lethal" dose varies widely from person to person and I have no doubt that consuming 40 or 60 mg of nicotine at a time is very dangerous. That's the same amount of nicotine as smoking 50-70 cigarettes or chewing ten to fifteen pieces of nicotine gum at the same time. That can't be good for you.
Boil some tobacco with water
The word you haven't thought about is "some". According to a different Wikipedia page:
It constitutes approximately 0.6–3.0% of the dry weight of tobacco[6]
Since plants are probably 70% water, that means that nicotine is roughly 0.2% to 1% of the wet weight of tobacco leaves. So to obtain three drops of pure nicotine (approximately 60 mg), we would need at a minimum 6 g of tobacco. That isn't very much! But keep in mind this calculation doesn't allow for any losses during extraction, and also I'm not sure if the Wikipedia figure for the nicotine content of tobacco refers to "fermented" leaves or to freshly harvested leaf tissue. So for a variety of reasons this calculation could be way off.
