In a word, inheritance. Taxa inherit their characteristics from their ancestors. So, just as children are generally more like their parents and close relations more like each other than distant relations, so species are usually more like their ancestral and closely related species than distantly related species. Yes, this is a simplistic statement, but it is a good place to start. It is worth spending some time considering what a character is, and what it is not.
Scientists do tend to use it in different ways.
If you are aware of the different meanings that it may have, you will find it easier to determine how a particular author is using it. A character is a feature that can be measured, counted, described, or otherwise expressed. It is an abstract entity. Petal color is a character. Plant height is a character.