Can someone explain the importance of a homeowners equity when trying to purchase their home.

[Brett Hannon]

I have been listening to the podcasts and reviewing the forums and keep hearing the importance of equity when evaluating a deal.  I don't understand why this is important to the invester when they are looking to purchase.  If the investor offers $140k for the property and its excepted what difference does it make how much equity they have? Does the equity only affect certain types of investing i.e. flippers, wholesalers,  or buy and hold? What am I missing here? 

Any assistance would be appreciated.