The definition of acceptability is to be something that is considered to be socially OK or within the realm of what is appropriate, or something that is tolerable but not necessarily desired.(adjective)
1. Being a single parent is an example of something that has gained more acceptability. 2. An example of acceptability is compromising with your spouse to keep the thermostat at 70 when you want it at 68 and he wants it at 72.