Why can't batteries be charged quickly? Charging of laptops, cell phones take so much time. Why can't we make such batteries easily/commercially which are charged more quickly? What's the thing behind this limiting?
 A: Typically batteries involve using the energy stored in some chemical compound (for example, we have batteries of type Lithium-ion). So what happens is we use the potential energy stored in the chemical as an electromotive force to power our device. 
Now what happens when allt he potential energy stored inside that compound runs out? We have to recharge it. In order to recharge it, we have to have a source that inputs energy into our system. This energy goes into the compound and reorients the atoms to their original positions, allowing it to store energy once again. Unfortunately, this process can take quite a bit of time, and it's very difficult to speed up. 
There you have it in layman terms. 
A: Mostly the problem is that in batteries, current flow is not by electrons as in something like a copper wire, but by physical movement of ions.  Only so many ions can migrate to the right place and perform the right chemical reaction over some fixed time.
A: Heat. Batteries have internal resistance and so produced heat when current flows through them (Joule heating). Also, the heat generated increases by the square of that current. E.g, doubling the charging current causes the heat produced to be increased 4 times.
Ultracapacitors are a different technology that can be used like batteries--they have very very low internal resistance and so can be charged or recharged at currents hundreds of times what you see in regular batteries like laptop ones. The tradeoff is that capacitors have really low capacity in comparison (they run out too quickly and must be recharged again).
