The target language is the language learners are studying, and also the individual items of language that they want to learn, or the teacher wants them to learn.
In a PPP lesson, the teacher first presents the target language, learners practise it, and then there is a production stage where the target language is used in a freer activity.
In the classroom
Lesson aims may be based around target language, e.g. 'Learners will be able to understand the difference between 'I didn't need to..' and 'I needn't have..'.