The English translation of "precio de oro por gram" is the price of gold per gram or gold price per gram. In this phrase "precio" is the word for price, "oro" is the word for gold, "por" means per and "gramo" is gram.
This phrase is commonly seen when trying to price out the value of gold, specifically gold jewelry or gold bars. There are online calculators that calculate the price of gold per gram or ounce. For calculators that do gold by the ounce the phrase would include the word "onza" instead of "gramo." These calculators can also do silver and platinum.