Carbon intensity - is the amount of carbon an activity produces - usually measured in grams CO2 per unit (eg per kW electricity/kilo of... etc). As a general rule the more energy used for an activity or product the more carbon intense it will be - because almost all our energy comes eitehr directly or indirectly from fossil fuels
Looking at 2 extremes, formula one car racing is carbon intensive and the fuel for the race is a tiny fraction of the sport's carbon/energy cost. The cars and equipment use high embedded energy (or carbon) materials with very short lifespans, and the sport is highly transport intensive, both directly, using airfreight and passenger miles and indirectly, by spectators press and media.
Punting down the Cam is about as carbon un-intense as recreation can get. The punt is made from wood - and is a natural carbon-sink, it's powered by human hands. Apart from the energy costs of the laundry of the odd unlucky punter who kept hold of the pole for just a little too long, its almost certainly a carbon neutral activity.
To account for carbon intensity both the embedded and direct carbon costs carbon costs need to be calculated - so the carbon intensity of driving includes the embedded carbon cost of the vehicle divided by lifetime mileage, the emissions per mile from fuel and a per mile cost for the infrastructure (roads, etc) needed to to run the car. These embedded energy costs almost double the carbon intensity of driving.
Looking of way to reduce carbon intensity is one of the best ways of reducing carbon footprints - so the carbon intensity of heating out homes could be reduced by reducing energy demand (improving insulation, better heating controls, better focused heating) or by heating more efficiently (solar water heating, heat pumps, high efficiency boilers,) or both - but option two doesn't use less energy - it just takes the energy in a more carbon efficient way (ie using a small amount of embedded energy and grid electricity to extract a lot of energy from the air or the sun)