Threads are the most important part of a process. They are the most common way to execute code in parallel and perform long-lived operations. Each time the application starts, a new process will be created with a main thread (a.k.a the UI thread). Inappropriate handling of operations like network access or database queries can lead to poor user experience or make the app unresponsive (blocking the UI thread which is responsible for drawing).
The Threads count graph shows when new threads are created and when they are destroyed. You can expect to see this value increase with operations that demand more processing on the device and decrease after the processing ends.