Consider the following scenario at a small business:
As a business owner I have 10k in the bank at the moment. I have a one time expense of 4k that will not directly impact the growth of my business. I can choose to pay the 4k out of the 10 in the bank and then put the rest towards business growth. Assuming a 10% annual return on capital at the end of this transaction I am left with $6,600.
Now if instead I chose to pay the 4k with a business credit card I have that only carries a 7.9% interest rate what would happen is that I incur a 4k balance that I have to pay off in a year and put 10k towards my business. Now, this is a simplified case that does not take into account the effective interest on the card and the minimum monthly payments. That being said, what happens in the end of the year is that I owe $4316 to my credit card but I now have 11k in the bank, due to business growth. That leaves me with $6,684 after a year's worth of operations, which is better than my original $6,600.
This is a small scale scenario though, but the basic idea is that if you can put the money towards growth that is better than the interest you are paying to the card, you win. The risks of course include missing a payment and incurring a penalty, not being able to grow your money at the rate you thought, and so on.
Hope this explains things a bit.