The MPU6050 is a Micro Electro-Mechanical Systems (MEMS) which consists of a 3-axis Accelerometer and 3-axis Gyroscope inside it. This helps us to measure acceleration, velocity, orientation, displacement and many other motion related parameter of a system or object. This module also has a (DMP) Digital Motion Processor inside it which is powerful enough to perform complex calculation and thus free up the work for Microcontroller.  

It is very easy to interface the MPU6050 with Arudino, thanks to the library developed by Jeff Rowberg. You can download the library from the below link

Jeff Rowberg MPU6050 Library for Arudino

Once you have added this library to you Arduino IDE, follow the below schematics to establish an IIC connection between your Arduino and MPU6050.