Database Page Evictions/sec is the rate that database file page requests, which require the database cache manager to allocate ...

Database Page Evictions/sec is the rate that database file page requests, which require the database cache manager to allocate a new page from the database cache, force another database page out of the cache.  The eviction count is charged when the page is allocated and not when the previous owner of that page was actually evicted from the cache.  If this rate is too high, the database cache size may be too small.