Learn Spanish (Latin America): Mi abuelo estuvo en el ejército.

This lesson teaches the passive voice (like "The letter was written by..."), which always uses ser. However, this sentence isn't passive! It is just stating someone's location or involvement. To say someone was physically in a place or institution like the army, Spanish uses estar, which becomes estuvo in the preterite tense.

Why use the preterite estuvo instead of the imperfect estaba if he was in the army for a long time?

Spanish uses the preterite (estuvo) when an event is viewed as a completed chapter in the past. Even though it lasted a long time, his time in the army had a clear start and end. If you used the imperfect (estaba), it would sound like you were setting the background for another event, like "My grandfather was in the army when he met my grandmother."

Why is the accent mark on ejército so important here?

The accent mark tells you to stress that specific syllable: e-JÉR-ci-to. It is crucial because without it, the word becomes ejercito (pronounced e-jer-CI-to), which is the "I" form of the verb ejercitar and means "I exercise." Missing the accent would completely change the meaning of your sentence!