To cotton on

To cotton on: to get to know or understand something.

Origin 
(from http://www.phrases.org.uk/meanings/cotton-on.html)

The phrase 'cotton on to', with the above meaning, appears to be limited in usage to the UK and other countries that were previously part of the British Empire, notably Australia and New Zealand. In the USA, especially in the southern states, 'cotton to' is used, with the slightly modified meaning of 'take a liking to'.

As early as 1648, in a pamphlet titled Mercurius Elencticus, mocking the English parliament, the royalist soldier and poet Sir George Wharton used 'cotton', or as it was spelled then 'cotten', as a verb meaning 'to make friendly advances'. 'Cotten up to' and 'cotten to' were both used to mean 'become friendly with'. Whether this was as a reference to the rather annoying predisposition of moist raw cotton to stick to things or whether it alluded to moving of cotton garments closer together during a romantic advance isn't clear. John Camden Hotten, in his Slang Dictionary, 1869, opted for the former derivation:

Cotton, to like, adhere to, or agree with any person; "to COTTON on to a man," to attach yourself to him, or fancy him, literally, to stick to him as cotton would.