Learn Turkish: Kursiyerlerin geldiği gün hava çok sıcaktı. - The weather was very hot the day the trainees arrived.

In English we say "the day when they arrived", but Turkish uses the -dik participle to modify words of time and place, such as gün (day), zaman (time), or yer (place). Even though gün isn't a direct object, the grammar works exactly like an object relative clause: geldiği gün acts like "the arrived-by-them day".

Why is the subject of the arrival kursiyerlerin (with a genitive ending) instead of just kursiyerler?

In Turkish relative clauses formed with -dik, the subject doing the action must take the genitive (possessive) case. Because the participle geldiği has a possessive ending on it, the subject "owning" that action needs to match it. You can think of it literally as "the trainees' arriving day".

Since kursiyerlerin is plural, shouldn't the participle be geldikleri instead of geldiği?

It can be, but it doesn't have to be! In Turkish, when a plural subject (like humans or animals) is explicitly stated in the sentence, the plural marker on the following verb or participle is completely optional. It is very common and natural to use the singular form geldiği here, though geldikleri gün is also perfectly correct.

Just a quick refresher: why does the past tense suffix change to -tı in sıcaktı?