The DS1307 is a real time clock device. This means that it will (once set) keep the current time. Generally, this will be used with a microprocessor so that the system will know what the correct time is when it reboots. Given that it is generally used with a microprocessor, the programmable square wave that the chip generates on pin 7 could be used for several things, but most likely (given the frequencies it outputs) it is designed to be timing pulses for serial communications. RS232 requires a regular clock, and that can be generated from this device if required.
For signal generators in general, they are used to stimulate circuits, for example testing filters, transformers and the like. Especially useful for testing a circuit when the correct input is not present.
Neil