First WHAT is spelled with an H... it is NOT wat it is WHAT
Second, A Country is an independent government that has it's own army, taxes, courts, etc. Other countries send ambassadors, it has passports and postage stamps, and a flag, etc. The best test of if something is a Country or not is if it can declare war.
Technically an Empire is a really big Country that is ruled by an Emperor. The difference is that a country is normally, though not always, made up of a single Nation. An Empire is made up of many conquered Nations.
To understand that, you need to understand what a Nation is.
A nation is a large ethnic and cultural group. The best way to tell if something is a Nation or not is if people identify themselves as being from it. For example The United Kingdom is not a Nation, but it is a Country.The United Kingdom has English, Welsh, Scotch, and some Irish in it... and if you meet someone from the UK and they won't say "I'm from the UK" they will say "I'm English" or "I'm Welsh" or "I'm Scottish" because that is the Nation they are from...but they are all citizens of the same Country.
Here is another example. Up until the late 1800s both Germany and Italy were not Countries, but they were Nations. These Nations were made up of dozens of tiny little Countries. All these Countries were part of the same Nation in that had the same language, culture, food, literature, customs and values, but they were all independent Countries. People talked about "The German Nation" when they meant "all those little German countries".
Sometimes a Nation will exist even if it has no country. Greece was conquered by Turkey in the mid 1400's, and the Greeks were ruled by Turkey... but they Greeks hung on to their language, their religion, their literature, their values, their heratige... and in the mid 1800s they revolted and became independent again. During the time they were under Turkish Rule the Greek Country did not exist, but the Greek Nation still did. The same thing happened to the Poles, and the Irish. For hundreds of years Ireland was part of the British Empire, but the Irish retained their nationality... their religion, their culture, their music, and in the 1920s they became independent again. Today the Ameircan Indian tribes are refered to as "Nations"... there is (for example) the Navaho Nation.
So most Countries are homelands of a particular Nation.
Ireland is the Country where the Irish Nation (or the Irish People) live. Israel is a Country that is designed to be a homeland for Jews. Norway is the homeland of Norwiegan people, Japan is the Country where the Japanese People live.
An Empire would be a country that conquered and took over lots of other countries. (See the other answer I wrote for you about how the Roman Empire had lots of other countries in it) and thusly would have people from many different nations within its borders.