Learn Turkish: Birlik eğitimdeyken çok yorulur. - The unit gets very tired while in training.

It is made of eğitim (training) + -de (in/at) + -y- (buffer letter) + -ken (while). Together, it literally means "while at training." Notice that -ken is attached after the locative case suffix -de, and because -de ends in a vowel, we must use the buffer -y- before adding -ken.

Why does the sentence use yorulur instead of yoruluyor?

Yorulur is in the simple present tense (the aorist), indicated by the -ur suffix. We use this tense to talk about general facts, rules, or habits. The sentence is saying that the unit generally gets tired during training as a rule. If we used the continuous tense yoruluyor, it would mean the unit is getting tired at this exact moment.

I know the adjective yorgun (tired). How is that related to yorulur?

They share the same root! The verb here is yorulmak, which means "to get tired." It is the passive/reflexive version of the verb yormak (to tire someone out). Yorgun is just the adjective form built from that same core meaning.

How does birlik translate to "unit"?

It comes from the number bir (one). The suffix -lik is used to create abstract nouns or nouns representing a group. So birlik literally means "oneness" or "unity," and is commonly used to refer to a military unit, a troop, or an association that acts as a single body.