Apple's newest phones only include a lightning jack. Since they have removed the headphone jack, you would need to use this jack in order to connect to regular headphones.
The lightning jack is a versatile connector, with which, you can charge your phone, transfer data, and listen to and control your music.
One of the biggest differences between the lightning jack and other types of connectors (like the USB-C standard) is that the lightning jack is an exclusively Apple design. This can be regarded as an advantage for Apple fans, as the products are generally under tighter control by Apple. But of course, this can also be a disadvantage as the consumer may have less choices for external devices and may face higher prices.
The lightning jack was originally released by Apple in 2012. It connects to devices similarly to the USB-C standard. That is, the connector is reversible. There is no wrong way to connect the wire.
Apple continues to use their own lightning connector instead of the USB-C for various reasons, which include Apple's ability to control the quality of connectors. In addition, Apple argues that this connector is "stronger" than the USB-C connector. This extra strength makes the lightning connector a better connect to docking stations.
Apple's lightning connector is an 8-pin connector. Each pin carries a digital signal for fast data transfer. The lightning connector can be used to connect peripheral devices (like cameras, mouses, etc.), it can be used to charge devices, and music streaming.
While Apple does save money through not having to license USB-C technology, there are some disadvantages for Apple users. Most notably, all other computers (including many Macs) and most other new phones use the USB-C standard. This means that in order to hook up a device through the port, you must either use a lightning to USB-C adapter or you must use a device that specifically is designed with a lightning connector. Due to lower supply and demand, lightning connected devices tend to be in lower supply and higher cost than traditional USB-C connected devices.