Raspbian is not a fail save power down operating system. This is because it uses extensive caching mechanism to increase performance as in general unix systems do it. So if you write data to the disk it is not really written to it (except the device is configured "pass through"). Instead it is hold in a buffer with a "dirty bit" set and written minutes later when the operating system is idle. If you just interrupt the power supply then it may be that you lost the data in the buffer. On next boot up the operating system detects with "dirty bit" set that there was an interrupted shutdown before and takes many effort to check failures and try to repair corrupted data on the storage. This take some time and may explain why you can start again only after some minutes.
But it is not guaranteed that the operating system can fix corrupted data. Depending on what you are doing it may work some time but you always risk to destroy your operating system. So never just unplug the power cord. Before doing it you should initiate a clean shutdown, for example with:
~$ sudo systemctl poweroff
Then the operating system has time to write all buffered data to the disk and unmount them and do other important things for saving the status.