Huffy cranbrook popping
Going out on a limb, my guess is that the chain is too tight.  

I've seen (heard) this issue on many bikes like this. On about 98% of big box store bicycles are sold with all the bearings and the chain too tight and the tires too low on air.

How tight should it be?:


  The chain slack on a bicycle ... is quite critical, and is regulated by moving the rear axle back and forth in the forkends. ... The chain should be tight as it can be without binding. If the chain is too loose, it can fall off  


Later in the article:


  When adjusting the chain, you need to be able to turn the cranks. With a fixed gear or coaster brake, the rear wheel has to be off the ground. Keep your fingers away from the sprockets: the momentum of the rear wheel can crush a finger caught between a sprocket and the chain.
  Sheldon Brown, Minimizing Chain Slack


Assuming the chain is too tight you'll want to loosen the chain just enough to make the popping stop. 


Loosen the chain side axle nut and push the tire to the side so that the chain is gains a little slack. 
Snug the chain side axle nut up enough to hold (it does not have to be fully tightened yet) and test chain tension by pedaling (watch your fingers!) and listen for popping. 


If the popping is gone tighten the chain side axle nut fully. If not repeat steps 1 and 2 

After adjusting chain tension the wheel may not be in the center of the frame.


Loosen the non-chain side axle nut and center the wheel in the frame.
Tighten the non-chain side axle nut fully.


If the chain is not the cause of the popping sound no amount of loosening will make the popping go away.
What ever it turns out to be riding enjoyment and bike lifespan will be maximized if you have someone with some knowledge of bikes check it over from end to end.