Complex books support a higher level notion of a "Trade" that can comprise of multiple underlying positions, each of which can be more complex in itself; e.g. varying position size by scaling in/out.
Complex books should be used for more structured strategies such as pairs trading, options spreads, options combos (e.g. buy-write), hedging and other mechanisms.
Complex books also still support multiple concurrent trades, and tread the lifetime of each trade as starting from when the first underlying position is opened to when the last underlying position is closed.
Complex books are not supported by all brokers, and the functionality available varies more widely per-broker depending on the capabilities offered by each.