This is high precision real time clock by Adafruit based on the DS3231 IC made by Maxim Integrated. The datasheet of the DS3231 describe it as Extremely Accurate I2C-Integrated RTC/TCXO/Crystal and “it does exactly what it says on the tin! This Real Time Clock (RTC) is the most precise you can get in a small, low power package” as claimed by Adafruit.    without battery 

The reason for the high accuracy of this real time clock is explained as follows : “Most RTCs use an external 32kHz timing crystal that is used to keep time with low current draw. And that's all well and good, but those crystals have slight drift, particularly when the temperature changes (the temperature changes the oscillation frequency very very very slightly but it does add up!) The crystal of this RTC (DS3231) is inside the chip! And right next to the integrated crystal is a temperature sensor. That sensor compensates for the frequency changes by adding or removing clock ticks so that the timekeeping stays on schedule”. 

This is the finest RTC you can get, and now we have it in a compact, breadboard-friendly breakout. With a coin cell plugged into the back, you can get years of precision timekeeping, even when main power is lost. Great for datalogging and clocks, or anything where you need to really know the time. 

Specifications

• Complete the clock calendar function including the second, minute, time, week, date, month, and year
• + 2.3 V to + 5.5 V power supply voltage
• - 40 ℃ to + 85℃ temperature range
• Low power consumption

 

DS3231  Datasheet.

Detailed tutorial from Adafruit including arduino connection and code 

Detailed tutorial from  including arduino connection and code in pdf format.