This is the 4577th most frequent Chinese word.
殷
"殷" means prosperous, abundant, or fervent.
In this sentence, '殷' (combined as '殷实') refers to being wealthy or prosperous. It is used descriptively to denote material abundance.
他家殷实,生活极为富足。
His family is affluent, living a very prosperous life.
Here, '殷' is part of '殷商,' referring to the historical name of the Shang dynasty. It is a proper noun context.
在古代,殷商是一个重要的国家名称。
In ancient times, Yin Shang was an important name of a country.
In this case, '殷' (combined as '殷切') means earnest or eager, highlighting the intensity of the hope or desire expressed.