To understand how to do something. To be acquainted with all the methods required.

There is some doubt about the origin of this phrase. It may well have a nautical origin. Sailors had to learn which rope raised which sail and also had to learn a myriad of knots. There is also a suggestion that it comes from the world of the theatre, where ropes are used to raise scenery etc.

The first citation comes in Richard H. Dana Jr's Two years before the mast, 1840:

"The captain, who had been on the coast before and 'knew the ropes,' took the steering oar"

That clearly has a seafaring connection, although it appears to be using the figurative meaning of the phrase, i.e. 'the captain was knowledgeable', but without any specific allusion to ropes.

There are also early citations that come from the theatre. J. Timon, in Opera Goer, 1850 includes this:

"The belle of two weeks standing, who has 'learned the ropes'."

The nautical derivation seems more attractive and convincing, but the jury has to remain out on this one.