It's true that "strong verbs" could mean "irregular verbs" as suggested by others (and a quick search would give you similar information), but I think in your context, which is feedback on a piece of writing in a writing test, it makes more sense to understand this "strong verbs" as powerful verbs (also known as power verbs or power words) commonly used in essay writing.
I'm not familiar with calling these verbs "strong verbs", but, clearly, some people call them so. From a page on Sophia Learning:
Strong verbs create a detailed picture in the reader's mind.
weak verb: The lion is fighting with a zebra.
strong verb: The lion attacked a zebra.
Strong verbs convey a degree of meaning to the reader.
weak verb: The customer asked the clerk to check the price.
strong verb: The customer demanded the clerk check the price.
Strong verbs directly connect the subject to the action in the sentence.
weak verb: The car was washed by Mark.
strong verb: Mark washed the car.
BONUS: Even though each writing test may have its own criteria, we can assume that any writing tests share more or less the same criteria. In other words, they want to assess your writing ability. In IELTS Academic Writing, the four main criteria are:
- Task Achievement/Response (depending on the task)
- Coherence and Cohesion
- Lexical Resource
- Grammatical Range and Accuracy.
So, using the right word choices in your essay counts. If your word choices are too plain, the test examiner may understand that your lexical resource (i.e., vocabulary) is limited.
To demonstrate this point, let's weaken an example sentence on the IELTS Academic Writing description page!
Original (stronger): This criterion is concerned with the overall clarity and fluency of the message: how the response organises and links information, ideas and language.
Edited (weaker): This part is about seeing if the writing is clear, and if the test taker is fluent. We would like to see if the output has enough structure, and also if its information, ideas, and language go together well.
But, be warned! I'm not saying that you should aim at using the fanciest words you can think of in your essay! If you can't control them well, they'll know. So, make sure that you know these words well enough before using them in the test. Keep in mind that though words are important, other criteria are important, too, that is, whether your essay is strong or weak is not only about your word choices.