Metric MAP@k for what
MAP@k is normally used in recommendation systems, but also in other kinds of systems. Quoting from here:

If you have an algorithm that is returning a ranked ordering of items, each item is either hit or miss (like relevant vs. irrelevant search results) and items further down in the list are less likely to be used (like search results at the bottom of the page), then maybe MAP is the metric for you!

Some application examples are these Kaggle competitions:

Expedia Hotel Recommendations
Santander Product Recommendation
National Data Science Challenge 2019

And these are some resources with more information about it:

Mean Average Precision (MAP) For Recommender Systems

How mean Average Precision at k (mAP@k) can be more useful than other evaluation metrics