Transaction processing systems (TPS) directly support businesses by processing transactions that create or modify organizational data. TPS have four key characteristics - they provide rapid response, are reliable, are inflexible in processing standardized data, and enforce controlled processing through access rights. There are two types of TPS - real-time systems that immediately process transactions with instant confirmation, and batch systems that collect and process transactions in scheduled batches. Real-time systems have higher costs but provide benefits like concurrency controls and atomicity to ensure complete transactions.