It can refer to a few things, depending on the context:
* A woman who was involved in the Spanish Republic: This would be a woman who lived during the Second Spanish Republic (1931-1939) and supported its cause.
* A woman who embodies the ideals of the Republic: This would be a woman who is seen as strong, independent, and dedicated to democracy and equality.
* A title or honorific for a prominent female figure: This would be similar to "First Lady" in the United States, but specifically referring to a woman who is associated with the Republic.
The exact meaning of "mujer de la República" will depend on the context in which it is used.