What does it mean when a property listing says that the county denied for a "conventional" septic system
This is likely off topic on the site. You'd be better off talking to a real estate agent, or the local government. 

My guess is that they did a Percolation test (perc test), and the results came back as a fail.  This means that installing a septic system on the property is going to be a challenge, though they may have accepted alternative solutions in the area. If the lot has access to city/town sewers, you should be able to get hooked up to that.

Alternatively, the system may have been denied due to lack of space, too many other systems in the area, the system would be too close to ground or surface water, or some other local requirements were not met.

Depending on your area, you may be able to handle grey water without a septic system.  This would mean that you could have a shower, sink, washing machine, etc. You just wouldn't be able to have a toilet. Well, you wouldn't be able to have a toilet connected to a "conventional" septic system (whatever they consider "conventional"). There are alternatives ways of disposing of human waste, and the county may allow an "unconventional" septic system. You'd have to check with the county, to determine what would be allowed.

At any rate... If you're buying unimproved land, you're going to have to pay for whatever is built/installed on the property (septic system or otherwise).