This is the 648th most frequent Italian word.
stesse
"Stesse" is the third-person singular imperfect subjunctive of "stare," meaning "were" or "was" (subjunctive mood).
In this sentence, 'stesse' is used as an adjective meaning 'same', agreeing with 'persone' in gender and number.
Le stesse persone erano già presenti ieri.
The same people were already present yesterday.
Here, 'stesse' is used as a pronoun emphasizing 'condizioni', and appears in the subjunctive form aligning with the verb 'migliorassero'.
Vorrei che le condizioni stesse migliorassero presto.
I would like the conditions themselves to improve soon.
'Stesse' in this case is part of the present subjunctive conjugation of the verb 'stare', used in a hypothetical conditional clause.