The goals of ETA can be pretty well summed up by the English translation of the group's name.  The name, in English, is Basque Land and Liberty.  That is exactly what ETA believes that it is fighting for.

The Basques are an ethnic group without their own country.  They are native to the Pyrenees Mountains which are partly in Spain and partly in France.  Basque people live in both countries but are ethnically different than either the French or the Spanish.  In fact, their language is not even an Indo-European language and is, therefore, not related to any other language in Europe.

Because of their ethnic and linguistic differences, the Basques have long wanted to be separate from the countries in which they live.  This desire is especially strong in the larger Spanish part of the Basque country.  ETA has been conducting a terrorist war in an attempt to get the Spanish government to grant independence to Euskadi--the Basque country.