This phrase is used when you want to say that some conditions don't matter. The result, or your advice, will be the same in any of the conditions. For example:
No matter what she says, don't listen to her.
In this examply, your advice ("dont listen to her") is the same, regardless of what the person says.
You can use a dependent clause, like "no matter what she says", or you can use the word "happens", like in the example at top.
You can also use just the phrase "no matter what" to mean in any condition:
No matter what, I'll always love you.