How do you hash passwords with php?

How do you actually go through this process?

Let's say I have a password, "treehouse", which I want to store in my database. Storing it in a password column as "treehouse" is considered very bad practice. This I get. If someone gets into the database he gets access to all the passwords stored.

So for basic security, what you have to do is use php's

echo password_hash("treehouse", PASSWORD_DEFAULT);

//this will get me this following hash:
$2y$10$gVaZfNP5AK1ZLxYL0fBAIeX/H3z/lUCKNbCyoYqR7RZXNPCf94B1C

I then take that hash and store it in the database password column INSTEAD of "treehouse". I also store it somewhere in the php code for later comparison with user input. So the actual password "treehouse" is actually discarded, it won't be written ANYWHERE, in either database or php files. So the result would be something like this:

1. User enters password.
2. The user's input is stored in a variable and compared with the hashed password using php's password_verify("$userInput", $storedHash). (Usually in an if-statement).
3. If it's a match, it's the correct password.

PASSWORD_DEFAULT uses bcrypt but leaves room for when PHP updates or adds algorithms, so basically that's enough for basic protection? Have I finally understood this correctly?

Please halp this dumbfounded newbie! :=)