。
They keep a daily record of their business transactions.
Literal
Business [attributive-の] transactions [object-を] day [object-を] following [and-て] are-recording-[continuous-ている].
日を追って ('day by day') is an idiomatic adverbial phrase literally 'following the day' — using the verb 追う ('follow, chase') with 日 as a temporal marker. This pattern — noun+を+verb-te — is a productive way to form adverbials: 時を追って, 年を追って. 取引 ('transactions, deals') is the standard business word.