Setting nillable="true" means that the <birthDate> tag can appear as follows:
<birthDate xsi:nil="true"/>
However, since you also set minOccurs="0", you could also omit the <birthDate> tag completely from the XML and it would also still validate against your XSD.
Note that <birthDate/> or <birthDate></birthDate> is not considered null according to XSD rules.
Have a look at this great blog post for further reading.