Formal assessment uses formal tests or structured continuous assessment to evaluate a learner's level of language. It can be compared to informal assessment, which involves observing the learners' performance as they learn and evaluating them from the data gathered.

Example
At the end of the course, the learners have a final exam to see if they pass to the next course or not. Alternatively, the results of a structured continuous assessment process are used to make the same decision.

In the classroom
Informal and formal assessments are both useful for making valid and useful assessments of learners' knowledge and performance. Many teachers combine the two, for example by evaluating one skill using informal assessment such as observing group work, and another using formal tools, for example a discrete item grammar test.

Further links:

https://www.teachingenglish.org.uk/blogs/larry-ferlazzo/larry-ferlazzo-assessing-english-language-learners

https://www.teachingenglish.org.uk/article/evaluating-speaking

https://www.teachingenglish.org.uk/article/evaluating-speaking-part-2