HaShem means The Name. It represents the 4 letter unpronounced name of God which many mispronounce as "Jehovah" [I'm looking at YOU, Ceara!] and many think is pronounced "Yahveh".

Jews usually say Adonai, which means The Lord. Using "The Lord" was adopted my the Christians as well. Some very observant Jews will not use Adonai or "The Lord" unless it is during prayer or observance. The use HaShem or "The Name".

I like refering to the tetragrammaton as "The Name" more than as "The Lord" since it brings attention to that fact that it is a name and not a title. So this is almost always what I use.