I don't understand when people refi and "get their money back"

[Scott L.]

Please excuse my ignorance in this post, but I listen to podcast after podcast on my drive to work.

This morning I was listening to Bigger Pockets Podcast 210, about a younger couple starting out, purchased their first property a 4 plex and are house hacking.

The purchased it for like 400K, but down 45K and were cash flowing like 1K a month.

This is my question:  The guy on there said they then refinanced the mortgage 10 months after they bought the property and took out 50K, basically getting everything back that they put in it.  

I don't understand. People say that on the podcast none stop and I think its the theory around BRRR? But I don't get it? Aren't you then paying another loan on the amount you "take back out."

And if you use that money on something else isn't that just money you are paying an additional fee for?  I'm really confused about how all these people "get their money back out"

[JD Martin]

30 second example, using cash only:

Buy house for $100k. Put $25k into fixing it. Get it appraised for $160k. Get mortgage on house for $125k. You got your money back. The only equity left behind was the increase in value.

30 second example using mortgage:

Buy house for $100k with $20k down, $80k mortgage. Put $25k into fixing it. Get it appraised for $160k. Refinance mortgage to $125k. Pay off $80k mortgage and take back your $20k cash plus your $25k fixing it. The only equity left behind was the increase in value.

Capice?