Interlanguage is the type of language produced by second- and foreign- language learners who are in the process of learning a language. In language learning, learner’s errors are caused by several different processes. These include:
a. borrowing patterns from the mother tongue
b. extending patterns from the target language.
c. Expressing meanings using the words and grammar which are already known
From Richards, Jack C et al. 1992. Dictionary of Language Teaching & Applied Linguistics. Second Edition. Essex: Longman Group UK Limited. p.186

Interlanguage refers to the separateness of a second language learner’s system, a system that has a structurally intermediate status between the native and target language
Interlanguage is neither the system of the native language nor the system of the target language, but instead falls between the two; it is a system based upon the best attempt of learners to provide order and structure to the linguistic stimuli surrounding them. By a gradual process of trial and error and hypothesis testing, learners slowly and tediously succeed in establishing closer and closer approximations to the system used by native speakers of the language.
Inerlingual(Weinreich:1953) , Inerlanguage(Selinker:1972)
Synonyms: Approximative system(Nemser:1971),Idiosyncratic dialect(Corder:1971)
From Brown, Douglas B. 1994. Principles of Language Learning and Teaching. Third Edition. New Jersey: Prentice Hall Regents. pp.203-204

Selinker(1972) coined the term ‘interlanguage’ to refer to the systematic knowledge of an L2 which is independent of both these learner’s L1 and the target language. The term has come to be used with different but related meanings: (1) to refer to the series of interlocking systems which characterize acquisition, (2) to refer to the system that is observed at a single stage of development (‘an interlanguage’), and (3) to refer to particular L1/L2 combinations(for example, L1 French/L2 English v. L1 Japanese/L2 English). Other terms that refer to the same basic idea are ‘approximative system’ (Nemser 1971) and ‘transitional competence’ (Corder 1967)
From Roderick Ellis. 1994. The Study of Second Language Acquisition. Oxford:Oxford University Press. p.710

Teachers can give appropriate feedback after checking out learner’s interlanguage. Learners need not worry so much about making mistakes. They can assume that making mistakes is a procedure of development from mother tongue to Second Language.

The variable shape of interlanguage

The concept of interlanguage has had a majaor impact on the field of second language acquisition. Studies on interlanguage focus on the linguistic and psychological aspects of second language acquisition research.
I will first outline how the interlanguage assumption developed. Since the interlanguage concept is not only important for the development of the students‘ grammar system, I will then explore how it applies to other components of language. I will also focus on the consequences of the concept for the teacher and his work in the classroom.
Before the 1960‘s language was not considered to be a mental phenomenon. Like other forms of human behavior language is learnt by processes of habit formation. A child learns his mother tongue by imitating the sounds and patterns he hears around him. By approval or disapproval, adults reinforce the child‘s attempts and lead the efforts to the correct forms. Under the influence of cognitive linguists this explanation of first language acquisition was criticized. Language cannot be verbal behavior only, since children are able to produce an infinite number of utterances that have never heard before. This creativity is only possible because a child develops a system of rules. A large number of studies has shown that children actually do construct their own rule system, which develops gradually until it corresponds to the system of the adults. There is also evidence that they pass through similar stages acquiring grammatical rules. Through the influence of cognitive linguists and first language aquisition research the notion developed that second language learners, too, could be viewed as actively constructing rules from the data they encounter and that they gradually adapt these rules in the direction of the target language. However wrong and inappropriate learners‘ sentences may be in regard to the target language system, they are grammatical in their own terms, since they are a product of the learner‘s own language system. This system gradually develops towards the rule-system of the target language.
The various shapes of the learnber‘s language competence are called interlanguage. The term draws attention to the fact that the learners’ language system is neither that of his mother tongue nor that of the second language, but contains elements of both. Therefore, errors need not be seen as signs of failure only, but as evidence of the learner‘s developing system.
While the behaviorist approach led to teaching methods which use drills and consider errors as signs of failure, the concept of interlanguage liberated language teaching and paved the way for communicative teaching methods. Since errors are considered a reflection of the students‘ temporary language system and therefore a natural part of the learning process, teachers could now use teaching activities which did not call for constant supervision of the student‘s language. Group work and pair work became suitable means for language learning.

compromise system
approximative system
idiosyncratic dialect
learner language

When the learner is attempting to communicate in the target language, he employs a linguistic system distinct from the source and the target language.

There is a continuum from the source language through successive learning stages to the acquisition of the target language. For every stage there is an interlanguage, one for the learner's first attempts to communicate in the target language, one for his near-perfect use of it, and many more in-between. This evolutuon is presumably marked at every stage by systemic influence from the source language. It also represents an accretion of elements from the target language. The various stages can be defined in quantitative and qualitative terms.