'Lleísmo' refers to the convention in Castillian Spanish and most highland Latin American dialects to pronounce the digraph 'll' as a palatal lateral approximant or /λ/, which is basically the 'lli' sound in English 'million'. This is as opposed to the /j/ sound which it represents in most dialects (like the 'y' in 'yet'. Apparently, around the Seventeenth or Eighteenth Century 'll' was pronounced palatal lateral /λ/, and 'y' was pronounced palatal approximant /j/. Southern Spaniards (most of the ones who settled in the Americas) began to confuse the two sounds, both becoming /j/. This is why the older cities of the Americas, such as the capitals in the Andes like Lima and Bogotá still retain the lleísmo.
A person or dialect with lleísmo is described as lleísta (the opposite is yeísta). Due to the lleísmo, a distinction is made between valla/vaya, callo/cayo and llanto/yanto. This can, of course be very handy in avoiding confusion. There is a bit of prestige attached to it, but it's really just like how pronunciations of English can differ from Britain to America to Australia, and nowadays the lleísmo is less common in Castile than it was before, only existing in a very small, older, portion of speakers. It is, however, the standard according to The Spanish Academy, and is given in (Castillian)Spanish dictionaries as the pronunciation of 'll'. An interesting point is that if you speak to a British person in Spanish, chances are he or she has a lleísmo because the standard learned over there is the Castillian dialect, whereas in America the standard Latin American dialect is taught.