Lithium Battery Charger IC - Charging and Power
You MUST look at the diagrams in the data sheet and understand what they show. 

You must read the answers that people give and actually take note of what they say.
apalopohapa have you a completely clear answer.
You ignored what he said and just asked the question again.   

He said "The battery goes both to the charger and the circuit."

This means


The battery goes to the charger 


and


the battery at the same time goes to the circuit. 


If you read a sentence like that and it makes no sense then read it again (and again and again) - maybe draw a diagram - or simply look at the diagram in the datasheet.
It shows the output going to the battery
AND AT THE SAME TIME to the system load.  

And apalopohapa also said "When you are charging the battery, you are still powering the circuit."

This means


When you are charging the battery
you are still powering the circuit.


If that does not make sense then reread, rereread, rererereread.    

Look at this diagram.
The charger IC output is connected to the battery
AND
AT THE SAME TIME
The charger IC output is connected to the load.
It connects to the load and battery at the same time.
It connects to the battery and the load at the same time.
All 3 are connected together at once.
Does that make sense?