The word seize alone means to grab, take or confiscate. Therefore, seizing the day can simply means making the most out of an opportunity instead of waiting for another opportunity later
If you have a chance of having something done at the moment then you should go ahead and do it .
Other statements like Take the opportunity, use the moment, take the advantage can be used to express the same meaning.
An example in a sentence can be like; This is a new dawn, just get out of bed and seize the day.
From the sentence we can learn that whoever the statement is aimed at is being advised to grab any opportunities that present themselves.