This is the 30th most frequent Chinese word.
着
"着" indicates a continued action or state, or marks a grammatical aspect.
'着' in this sentence describes a current state or existence of an action or situation, in this case, books being placed in the room.
屋子里摆着许多书。
Many books are placed in the room.
Here, '着' reflects an accompanying or simultaneous action, describing how the main action, saying, is performed while smiling.
他笑着说：“没关系。”
He said with a smile, 'It's okay.'
The particle '着' here indicates a continuous action, 'listening', which is ongoing at the moment.