I have crafted a Barbarian bugbear that uses a halberd weapon, and will take Polearm Master as a feat.
When you make a melee attack on your turn, your reach for it is 5 feet greater than normal.
The description of the Reach weapon property says:
This weapon adds 5 feet to your reach when you attack with it, as well as when determining your reach for opportunity attacks with it.
I am trying to determine the cut-off ranges for various situations. Making a standard melee attack is pretty straight-forward. He can attack anyone in 15' (5' for normal, plus 5' for bugbear, then add 5' for reach).
But how do I calculate opportunity attacks?
You can make an opportunity attack when a hostile creature that you can see moves out of your reach.
So my reach is generally 15'. But per the bugbear description, that extra 5' is only when I make an attack on your turn. So his effective reach is only 10'.
So an opponent can be next to the character and safely back away 5' because they have not left the 10'/15' reach. But what happens at 10' and 15'?
At 10', they are still within my normal reach, but only on my turn. At 15' they are leaving my reach, but I only get that extra 5' on my turn so it would not be available as a reaction.
P.S. There is a sister question about Polearm Mastery and entering my threat range.