In the pledge of allegiance what does and to the republic mean?

it refers to the United States of America
A republic is:
1 a (1) : a government having a chief of state who is not a monarch and who in modern times is usually a president (2) : a political unit (as a nation) having such a form of government b (1) : a government in which supreme power resides in a body of citizens entitled to vote and is exercised by elected officers and representatives responsible to them and governing according to law (2) : a political unit (as a nation) having such a form of government

source:
http://www.m-w.com/cgi-bin/dictionary

the powder keg