In software development a transaction generally refers to a communication that has built-in assurance checks and can be "rolled-back" upon failure. This applies most commonly to database communications, but the concept of transactions can also extend to other forms of communication like HTTP.
Transactions are a way to handle sensitive data. The most common example is a financial transaction. If an error occurs while withdrawing funds from an account, it is unacceptable for that error to double withdraw funds or never withdraw any. These are the types of problems we use the broad term transaction management to describe.