Google Play hosts a number of applications that focus on local network traffic sniffing for Android devices, but for the majority of them you would first need to root the device. I worked on a project where I needed a quick glance on what networking requests an Android application does in the background, so the easiest way was to setup a local sniffer on the device itself.
tPacketCapture is a free application developed by Japanese company Taosoftware and distributed through Google Play. Its main benefit is that it doesn’t require a rooted device, as it cleverly uses the built-in VpnService provided by the Android operating system. VpnService creates a virtual network interface and, by using this method, no root permissions are needed for packet capturing.