Hearing the word 'swot' conjures images of Just William, silly uniforms, grumpy teachers and girls in pigtails.
A swot is a person who devotes a lot of time to studying, but it doesn't have the same connotations as a nerd. Rather, a swot normally has low confidence, and learns things by rote. The swot may be the person who gets the best marks in the exam, but you know she had to work for them.
The word 'swot' started off as 19th Century military slang. 'swot' is a variant of sweat. One theory even claims that is was at Sandhurst that the professor of Maths, one William Wallace, first used the expression "It mades one swot", and the word caught on from there. Certainly, in 1850, soldiers used the word to mean mathematics. It then extended to the people who studied it, and from there to people studying in general.
Swot is also a verb. To swot up is to study, often a specific subject for a specific purpose. Swotting up before an exam or interview is common. The 'up' can be dropped, but its usually there.
'Swot' is generally considered an insult, or at least not something anyone would want to be. The image of the unpopular school swot, alone with his books and ignoring the world, was reinforced by children's books of the first part of the 20th Century, as well as comics like the Beano and the Dandy. Swotting up, though, is quite acceptable, as it's a bit like cramming, and implies the swotter has left everything to the last moment.
Perhaps because it originated as a spoken word, swat is sometimes used as a variant spelling. While used universally throughout Britain, as well as in South African English. It's used in Australia and NZ, but not commonly, and mainly the verb form. In Ireland, they tend to spell it 'swat'. I suspect that Americans don't use it at all.
(not sure about Canada; let me know).
cf. The Oxford English Dictionary
Thanks to CloudStrife, StrawberryFrog, sneff, and Mogest.