user54311: Circuit explanation- 

Arduino Uno connected to multiple sensors and to 16 x 2 LCD.
Uno's TX pin to ESP-01 RX pin.
Uno has been programmed to read values from sensors and display them on LCD along with printing them on Serial Monitor.
ESP-01 has been programmed to receive values from Serial Monitor and transmit it to ADAFRUIT MQTT server.

Problem - 
However when i am using USB to power the Uno it is successfully displaying data on LCD as well as to Serial Monitor and values are succesfully being send on the MQTT server after being read from Uno's serial.
But when Uno is battery powered, serial communication stops.
I have tried adding 2 decoupling capacitors of 100uF to 12V battery supply. Battery are rechargeable cells. 
What could be the issue? 

user42015: I will put the solution from the comments into an answer.
All devices, that should interact through electrical wires with each other, must have a common ground. Ground is the point, from which the voltage is measured, and the devices need a reference, that is not only valid for themselves, but also valid for the communication partner.
You can think of the following analogy: Image that you and a friend have each one ball, that you are throwing into the sky (a positive height/voltage) and catching it again (zero height/voltage --> ground). While you stand on the parking lot, your friend is standing on a high building. As long as you both only play this with yourself, it is easy for you to throw and catch the ball, because you can easily measure the height of the ball and it will always behave the same. But know imagine, that you want to play together. The height/voltage, that your ball reaches is still positive for you. But from the perspective of your friend it will look, like a large negative height/voltage. How should your friend interpet that and how should he now play with you?

In some electrical circumstances you don't want to connect the grounds of two devices together (maybe because of noise on the ground line). Then you have to achieve galvanic isolation, so no electrical connection between those two. An optocoupler is a device, that can achieve this. Basically it's just an LED and a phototransistor in one casing. From one device you power the LED. Due to the LEDs light, the phototransistor (which is connected to the other device) will become conductive. In combination with a pullup/pulldown resistor on the phototransistor you can have communication without common grounds.

54311: <p>Circuit explanation- </p>

<ol>
<li>Arduino Uno connected to multiple sensors and to 16 x 2 LCD.</li>
<li>Uno's TX pin to ESP-01 RX pin.</li>
<li>Uno has been programmed to read values from sensors and display them on LCD along with printing them on Serial Monitor.</li>
<li>ESP-01 has been programmed to receive values from Serial Monitor and transmit it to ADAFRUIT MQTT server.</li>
</ol>

<p>Problem - 
However when i am using USB to power the Uno it is successfully displaying data on LCD as well as to Serial Monitor and values are succesfully being send on the MQTT server after being read from Uno's serial.
<strong>But when Uno is battery powered, serial communication stops.</strong></p>

<p>I have tried adding 2 decoupling capacitors of 100uF to 12V battery supply. Battery are rechargeable cells. </p>

<p>What could be the issue? </p>
 42015: <p>I will put the solution from the comments into an answer.</p>

<p>All devices, that should interact through electrical wires with each other, must have a common ground. Ground is the point, from which the voltage is measured, and the devices need a reference, that is not only valid for themselves, but also valid for the communication partner.</p>

<p>You can think of the following analogy: Image that you and a friend have each one ball, that you are throwing into the sky (a positive height/voltage) and catching it again (zero height/voltage --> ground). While you stand on the parking lot, your friend is standing on a high building. As long as you both only play this with yourself, it is easy for you to throw and catch the ball, because you can easily measure the height of the ball and it will always behave the same. But know imagine, that you want to play together. The height/voltage, that your ball reaches is still positive for you. But from the perspective of your friend it will look, like a large negative height/voltage. How should your friend interpet that and how should he now play with you?</p>

<hr>

<p>In some electrical circumstances you don't want to connect the grounds of two devices together (maybe because of noise on the ground line). Then you have to achieve galvanic isolation, so no electrical connection between those two. An optocoupler is a device, that can achieve this. Basically it's just an LED and a phototransistor in one casing. From one device you power the LED. Due to the LEDs light, the phototransistor (which is connected to the other device) will become conductive. In combination with a pullup/pulldown resistor on the phototransistor you can have communication without common grounds.</p>
