I understand it loosely as government spending hurting businesses, but I can't explain the mechanism.
Accepted answer
Crowding out is the chain from deficit-financed government spending to reduced private investment.
The government borrows to fund a deficit, which increases demand for loanable funds. That raises the **real interest rate**. A higher real rate makes borrowing more expensive for firms and households, so private investment spending falls.
Show it on **loanable funds**: demand shifts right, real interest rate rises, and you point to the reduced quantity of private investment. In your write-up, name each link — borrowing → higher real rate → less private investment — because credit usually comes from the mechanism, not the phrase itself.