Open-mindedness is the quality of having a mind that is "open" to new ideas, especially ideas which may challenge one's existing beliefs.
There are a number of views on this quality, with some people (predominantly liberal) viewing it as a strength and others (predominantly conservative) viewing it as something of a liability if not used with great caution.
The Open Mind and Liberalism
Conservatives often see open-mindedness as synonymous with liberal decadence and the decay of morality in society. Individuals who are "open to new ideas" may lack the moral judgment to distinguish good/moral ideas from bad/immoral ideas, and may choose immoral ideas and practices because they are appealing in the moment or lead to personal gratification.
The Open Mind and Conservatism
Many see open-mindedness as innately hostile to certain aspects of conservatism, as one of the basic underlying ideas of conservatism is that existing social structures (institutions, principles, moral codes, etc.) have embedded wisdom on which we depend but which we do not understand, and that tampering with those structures may cause them to fail in ways we cannot repair.