What Danno has stated —
The Hebrew translates to "all the families of the earth shall be blessed in you." The issue would be to understand what it means to be blessed "in" not "through" you. This is often understood simply to mean "using your name" or "with your name" as in "may you be like Abraham".
— is the explanation of Genesis 12:3 according to its plain meaning as found in Rashi.
But there is a point that should be emphasized. This covenant is being made to Avram, meaning Avraham before the covenant of circumcision. Like it states, all the families of the earth that bless Avram (in his efforts and mission) will be blessed by the Creator. And those that curse him will be loathed (אאר). It says that Avram together with his wife, Sarai and the 'souls which they had made there in Charan', meaning those people who had come to serve the Creator like Avram, according to the faith of Shem (meaning keeping the 7 commandments of Noach) departed for the land.
Rashi explains that at this point, Avram, who was a direct descendent of Shem, was being told by the Creator to leave the land of his birth (Ur and later Charan) and to go to the land that G-d would show him.
It says that this land was occupied by the 'Canaanites' (which means traders or merchants) at this time. As Rashi explains, the land of Israel had originally been given by the Creator through Noach to his son, Shem. These foreign merchants had come to the land of Israel from their original home and subjugated its inhabitants, the descendants of Shem, and taken up residence. Avram was being told to go as a rightful heir to Shem and reclaim possession of this land for his future descendants as the Creator had originally intended.
These occupying merchants were called 'Philistines' (from the word פלסטון which means 'fraudulent in business'. It also is associated with the idea of being 'extreme' from the root פלש as in פלשתי. Midrash describes how they initially established these trading outpost by using their women in forced prostitution. This is what initially lured the customers to come and do business.) This was connected to their worship of the 'snake goddess' called 'As-sa-sa-ra' which seems linguistically to be the source of the prohibition of worship of 'Ashera' mentioned in the Torah. They were originally called Kaftorim by the Egyptians.
According to current archeological evidence they appear to be part of the Minoan civilization, an early Mediterranean seafaring nation that was in direct competition with the Egyptians. They practiced human sacrifice and were reputed to be powerful warriors known for their expertise with a type of sling which was secured to their heads. Recent digs around the Aegean have shown evidence that they practiced cannibalism. They had trading outposts along the coastline all around the Mediterranean with their home based in the Aegean on the islands of Crete, Karpathos (as in 'Kaptorian') and Santorini. They were incredibly successful and despised by many of the other nations in the area. The Minoan civilization was destroyed by an act of G-d through the eruption of Thrace and the ensuing multiple tidal waves around 1613 BCE. The remnant of this civilization tried to make permanent settlements around the Mediterranean including the land of Israel. See the following links for some of these details.
The verb for 'loathed' (ארר) which is the consequence of cursing Avram in his mission is unusual and has a distinct meaning. (קלל means 'to make easier' or 'to lighten' and the opposite of this is קללה which means 'to curse' or 'to make more difficult'). 'Loathe' on the other hand has a meaning of 'disappearing' or 'ceasing to be revealed'. This can be seen in the commentary of Ramban on Genesis 4:11 and the Shadal of Exodus 22:27. This can also be seen in Yerushalmi Sotah discussing the ink that is erased in the water which a suspected adulteress will drink.
In context, this means that those peoples of the earth who assist the inheritors of Avram's task to take possession of the land of Israel, meaning those people who help the Jewish people, will be blessed with continued good life and existence. This who hinder and obstruct this mission will, like the letters that are erased in the waters of the suspected adulteress, disappear from the world and cease to receive the blessings of life from the Creator.