By Karen Stanley
Although a number of people had talked about the types of interim grammars someone develops in the process of learning a second language, the term "interlanguage", coined by Larry Selinker in 1972, is the name that has stuck.
Although theories involving interlanguage have evolved, developed, expanded, etc., over time, one important element is the concept of the learner trying out different hypotheses for phenomena which the learner has observed in the target language. Here's a rather simple example of a hypothesis:
When I was learning French, I initially thought that the word for dictionary was "larousse," because people were always saying to "Go get the Larousse." As French speakers on the list will know, "Larousse" is simply the publisher, and for a long time was like "Websters" used to be in the US, almost the only one anyone used.
Another I see in my students is the idea that you put "was" in front of any verb to locate the action in past time - eg, "He was go to the story yesterday." Of course, learners form many much more complex hypotheses about formation of grammatical structures, use of tenses, etc.
I personally disagree with the concept of a Universal Grammar (often referred to as UG, pronounced 'you-gee', although I sometimes privately think of it more with an "ugh" bias), developed by Noam Chomsky, as being hardwired into human beings. I think that the elements of interlanguages can all be accounted for in other ways than by thinking human beings are born with a knowledge of grammar in their brains.
I find a newer theory, now called Connectionism or Connectionist Theory, but previously referred to as PDP (parallel distributed processing - I think I've got this right). Anyway, very briefly, this bases ideas of language acquisition more on the same types of properties that allow learning in general. Part of that theory is that each repetition lays down memory, and as repetitions with all their variations build, certain connections in the brain are strengthened. People have written books on this, so two or three sentences hardly explains the whole idea.
A good basic reference textbook about many basic theories, ideas, factors, etc. of Second Language Acquisition (SLA) is Rod Ellis's 1994 volume (Oxford University Press), "The Study of Second Language Acquisition." It's 824 pages, but the way he presents ideas is accessible (I think) to people without much if any formal training in SLA. ISBN 0-19-437189-1
A basic introduction to interlanguage is: http://www.geocities.com/coolsla_2000/interlanguage.htm
In TESL-EJ, there's an interesting review of a book on aspects of SLA in general; it includes quite a bit of actual information, but I'm not sure how easy it would be to take it all in if you don't have much background. Still, worth a look, I think:
Another general background paper that I thought might be accessible is:
One that briefly outlined 'interlanguage' and some other concepts at a pretty basic level is: