the long version saying the same thing:
That computer is a battery-CAPABLE device. It is not optimized as a battery-operated device. (It is NOT an iPhone.)
Your computer performs best when connected to AC power, such as the power adapter. It can use the full output of the Power Adapter AND when doing especially challenging work will also freely "borrow" power from the battery. In some cases, even with the power adapter connected, the charged state may decline during very stressful work.
When used only on battery, your computer has no extra cushion of power, and may perform more slowly. However, for ordinary non-stressful tasks this may not be objectionable (possibly not even noticeable.)
In general, you should ALWAYS connect a power source when it is possible to do so, and only run on batteries (which could be somewhat slower) when no power sources are at hand. Your Mac maintains its battery charge levels under program control, and will NEVER over-charge.
That blocky device that plugs into the wall is the POWER ADAPTER. I am not trying to be a jerk about terminology, what these boxes do and how they do it is essential for understanding how they all work together. The LEDs in the MagSafe end are controlled by commands from the computer.
The CHARGER is inside the MacBook Pro, and is completely under program control. Your Mac accepts some power when needs to run, and accepts more power when intends to charge its internal battery. A power source like the Power Adapter can not 'force itself' on your MacBook Pro. Only the algorithms inside your Mac can decide when is a good time to charge the battery.