What is considered a cash offer?

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I'm feeling insecure about this question because it sounds simple, but

What is considered a cash offer in a real estate transaction?

My wife and I are looking at buying two rental properties in our area that are owned by the same investor. They've been on the market for several years and are in need of repair. Our strategy is to make a combined cash offer for both properties in hopes that a speedy close and getting two properties off their hands will net us a pretty deep discount. 

I'm working furiously to line up my ducks to have the cash money ready if they accept. I thought hard money and family money with a conventional refinance after the properties are fixed up was the way to go, but now I'm unsure. After reviewing a few HML loan program details, I'm confused if the loan would be considered cash.

Is a cash offer simply having the money in my bank account prior to the transaction and that you just have to close with a lender prior to the transaction?