This term is used in two different ways. One use is to identify the language, e.g. Mandarin, Arabic, Spanish, English etc that a learner is trying to learn.
Another use is to refer to the particular item(s) of language that a teacher selects for learners to learn in a particular lesson and which the activities and materials in a lesson aim to teach.
Example
Some target language for a lesson for elementary learners might be:
the irregular past tenses went, took, came, sold, bought, saw, said, found in affirmative, negative and interrogative forms
or
exponents for suggesting: why don’t we../ how about +gerund/ we could…./ what about + gerund
or
vocabulary from the lexical set of clothes: jeans, top, shoes, sandals, sweat-shirt, jacket, scarf, coat.
Further reading
Bolton, K. and Kachru, B. (2006). World Englishes, Critical Concepts in Linguistics, Volume 5.
Scrivener, J. (2011). Learning Teaching, 3rd edition. London: Macmillan.
http://www.willis-elt.co.uk/taskbased.html
http://www.teachingenglish.org.uk/knowledge-database/target-language
https://www.cambridge.org/elt/resources/appliedlinguistics/reading/WorldEnglishes_Sample_Ch3.pdf