This is the battery clip connector used in the radio kit. The hard plastic backshell is of a higher quality than you might see used elsewhere. It is intended to connect to a small rectangular 9 Volt battery commonly used in smoke alarms. PP3 is the common, ancient designation for those batteries used in England. (Ever Ready Power Pack 3) You may see the shape also denoted by MN1604, though that also suggests that it is an alkaline type rather than an old cheap zinc chloride type. It is much better to use an alkaline type for the kit. It will last longer and is better value.
Using a fairly small battery reduces the maximum amount of current that it can provide. This is handy in case there's a mistake made in positioning the components that produces a large current draw. It's fairly difficult to destroy the silicon transistors by inserting them the wrong way round if using this type of battery.