Energy intensity (abbreviated EI) measures how much a bit of energy benefits the economy. This value is calculated by taking the ratio of total primary energy use (TPES) (all of the fuels and flows that a country uses to get energy) to GDP (the total money made in a country). This quantity (measured MJ/$) is used to indicate how effectively a certain economy is using their fuels and flows. When a country reduces wasted energy it becomes more efficient, this lowers its EI (lower EI is better).
This ratio quantifies how much good a little bit of energy provides. Energy use per capita describes only how much energy is being used, and provides no details as to how that energy is helpful. EI clarifies 'what energy does for a person', which certainly varies from country to country. Wealthier countries almost always use more energy per capita than poor countries and EI accounts for this discrepency in wealth.
The economies of countries around the world benefit from having access to energy infrastructure. EI describes how well this infrastructure is doing it's job. Below is a map showing the relative energy intensities of countries across the globe.
EI is calculated by adding up all of the primary energy sources that a country uses (TPES). This adds all of the raw forms of energy (coal, wind, natural gas, energy found in natural resources, etc.) before they are converted to energy currencies like electricity.  The amount of these raw forms of energy (fuels and flows) includes everything that's been imported, but does not include any energy that was exported. The amount of energy used to calculate EI is only the energy that the country uses as energy. For example, if a country produces a barrel of oil, and sells it to another country, that would be a commodity that the country is selling and wouldn't be part of the energy intensity calculation. Imported oil that's used for energy would be. Below is a graph showing how the two indicators for energy intensity, GDP and total primary energy supply (TPES), have changed for countries over time relative to a normalized year (the first year data is available).
Although EI is a valuable way to describe how well a country uses energy, there are drawbacks to using EI. First, there are different accounting methods to determine total primary energy used. Additionally, GDP does not always directly correspond to the welfare of a country (see problems with GDP). When discussing EI, it is important to consider factors that affect a country's economy. For example, countries that have a economies based on extracting natural resources often use more energy because mining resources is very energy intense, making for a relatively poor EI. Also, manufacturing takes a tremendous amount of energy, for the amount of money that's made from exporting those goods. A service based economy, like a country with an industry based on banking or computer programming, tends to be less energy intensive, so has a better energy intensity. Other factors like size and climate of a country can also play into EI.
EI does give some indication for how efficiently economies are able to harness primary energy. A low energy intensity is desirable—as it indicates an effective energy infrastructure. For example, large scale power plants tend to be more efficient than small generating stations (although cogeneration can provide exceptions). Governments often aim to improve energy intensity by targeting energy efficiency (replacing traditional light bulbs with CFL light bulbs and LED light bulbs). This improvement in energy efficiency does reduce the EI for a country, and is much of the current strategies in combating climate change. Improving EI is important as it encourages more economic activity and GDP growth so that a country can prosper, but not rely on increased energy consumption to create this growth.
Most people would prefer to maintain economic prosperity, while taking care of environmental concerns. EI is more meaningful of a measurement than energy efficiency because it includes the idea of how well a country is doing. At a personal level, energy efficiency tends to be easier to understand, so people focus on that more.
Generally, EI gets worse during the early stages of industrialization as economic advancement uses less effective equipment. There is also quite a bit of embedded energy needed for the energy infrastructure like the grid. After this rapid industrialization, the EI gets better as technology and infrastructure improve. This infrastructure includes having paved roads, and buildings with a fair amount of steel. Once this is put into place, maintaining these assets is much cheaper (both in terms of money and energy use) than putting them up in the first place. Other ways of lowering EI include advancing methods of extraction of raw materials and increasing the efficiency with which production materials can be obtained. Recycling aluminum can dramatically improve EI because so much energy goes in to making aluminum in the first place.
The countries with the best energy intensities are Switzerland and Japan, meaning that they use the least energy to produce a unit of their GDP. These economies are not heavily reliant on resource extraction, so it's not necessarily fair to compare them with countries like Canada.