A century is a period of one hundred years. A century may also describe one hundred of something else, like a score in a sports game. The building in the picture was built more than two centuries ago.
Day might refer to the time when the sun is up, for example, "my cat sleeps all day", or it might mean an entire 24 hour period, usually counted starting from midnight. The opposite of day is night.
A month is one of twelve parts of a year. Not all months have the same number of days. The months are: January, February, March, April, May, June, July, August, September, October, November, and December.
Present is another word for gift. Present also means the current time, right now. It is used in some sayings: "There's no time like the present".
A reign is the time that someone is in power, or the act of them being in power. For example, "the King reigned for twenty years". Words that sound the same as reign but are spelt differently are rain and rein.
A second is a unit of time. There are 60 seconds in a minute. Second is also the number two place in a competition.
Time is how you measure the order that things happen. Time that has already happened is the past, and time that is yet to happen is the future. Time is measured in units like hours, days and years.
Today is the current day, right now. Or you could be talking about the present era, like "today we find our information on the Internet".