as a noun, 'matter' primarily refers to a physical substance or material, or it can refer to a subject or situation under consideration or discussion.
Everything around us is made up of matter.
What's the matter? You seem upset.
The matter of security was discussed in the meeting.
the phrase 'for that matter' is used to emphasize that a particular thing also applies to what you have just mentioned. 'Matter' in the context of physics has a specific definition, referring to anything that has mass and occupies space.
as a verb, 'matter' means to be of importance or significance.
Your opinion really matters to me.
It doesn't matter if we're a few minutes late.
Why should it matter to anyone else?
'matter' as a verb is often used in questions and negative statements to discuss the importance or relevance of something.
Be cautious not to confuse 'matter' (to be of importance) with 'madder' (more mad or angry).