As a noun meaning "physical substance":
* The scientist studied the properties of dark matter.
* The table is made of solid matter.
As a noun meaning "importance":
* It doesn't really matter to me what you choose.
* The matter of the missing funds was taken seriously.
As a verb meaning "to be important or significant":
* It matters to me that you are happy.
* Does it matter if we're late?
In a phrase meaning "to be of importance":
* It doesn't matter how you get here, just get here on time.
* The matter of your health is of utmost importance.
As a verb meaning "to be concerned about":
* I matter to my family.
* You should matter to yourself.
You can also use "matter" in more complex sentences, like:
* The fact that the universe is expanding matters a great deal to our understanding of physics.
* It doesn't matter what you say, I won't change my mind.
The specific meaning of "matter" will depend on the context of the sentence.