When the counter value reaches the specified milestone number, a commemorative message will be displayed.

Literal

Counter [possessive-の] value [subject-が] specified 'milestone-number' [to-に] became-[when-たら] commemorative-message [object-を] display-[causative-させます].

Early-web culture: キリ番 (kiriban, milestone number) refers to round counter numbers like 1000, 10000, etc. that visitors would celebrate. 表示させる is the causative of 表示する — 'make (the system) display.' A nostalgic sentence from the era of homepage hit counters.