After a training session you increase the metabolic demand on the body. That is, by breaking down muscles during strength training, you are sending a signal that they have to adapt and get stronger. They do so by increasing anabolism; water goes into the muscles to produce more efficient chemical processes, amino acids follow, waste products are removed. All of those processes are driven by the supply of blood; anytime you have a stress on the body, be it psychological or physical, the body tries to adapt. In order to do that it must increase blood supply.
I run one hour without a break everyday. Am I over training? You might also find my answer to this question intresesting as it pertains to your question.
Also, as Dave says in the comment, one of the reasons is an increased sympathetic drive. That effect is not as long lasting though, but it does have its part. I would urge you to read up on "heart rate variability". There is lots of good research on the topic. Basically, it depends on the ratio between your parasympathetic and sympathetic drives.
During training you increase sympathetic drive; the body goes into fight or flight-mode. During that time it cannot regenerate. That is, the body remains in a catabolic state. And the pulse is higher. The sooner you recuperate your parasympathetic drive, the sooner the body can start regenerating, strength can increase, and the pulse can fall back to pre-training values. One well known way of regaining that ratio is by doing a cool-down. Eating also helps. But from what I've seen in litterature, the best method by far is Cold Water Immersion. There is even research showing that just having your face washed with cold water for a couple of minutes regenerates heart rate variability and thus speeds up recovery.
