Here’s an explanation from the W3C (link):
The following algorithm describes how the two properties [min-height and max-height] influence the used value of the ‘height’ property:
The tentative used height is calculated (without ‘min-height’ and ‘max-height’) following the rules under “Calculating heights and margins” above.
If this tentative height is greater than ‘max-height’, the rules above are applied again, but this time using the value of ‘max-height’ as the computed value for ‘height’.
If the resulting height is smaller than ‘min-height’, the rules above are applied again, but this time using the value of ‘min-height’ as the computed value for ‘height’.
To summarize: Basically, if the min-height is greater than what the height would otherwise be (whether an explicit height is specified or not), then the min-height is used as the height. If the min-height is less than what the height would otherwise be, then the min-height has no effect.
For the specific case you give, specifying height:100% makes the height of the element equal to the height of the containing block. (However this could potentially be overruled, for instance if you also specified max-height:50%.) Specifying min-height:100% means that if the computed height is less than 100%, in fact even if you explicitly specified a height less than 100%, it is treated as if you said height:100%. Note that one key difference is that max-height can overrule height but cannot overrule min-height (because max-height is considered after height but before min-height according to the W3C recommendation as quoted above).