Hostility is the state of ill will and bad feeling. If a teacher embarrasses you in front of the whole class, you will probably regard him or her with hostility for the remainder of the school year.
Hostility can be used to describe aggressive relations between two countries as well as between people. The issue of territorial borders can often cause hostility between neighboring countries. If actual fighting breaks out, use the word hostilities to refer to the violent actions between them. The ordinary citizens of the countries involved will look forward to the end of hostilities when the two governments are able to work together for peace.