Academic Rigor

How would you define "academic rigor"?  It is something I always thought I wanted for my children: academic rigor.  One of my favorite homeschool resources (WTM forums) has discussions often about Academic Rigor. It is usually seen as a good thing.  I looked up the word "rigor" on Dictionary.com, and here are some of the definitions of rigor:

1. strictness, severity, or harshness, as in dealing with people.

2. the full or extreme severity of laws, rules, etc.

3. severity of living conditions; hardship; austerity: the rigor of wartime existence.

4. a severe or harsh act, circumstance, etc.

 

Rigor even describes plants living in an unsuitable environment for growth:  inactivity, stagnation, inertia.

Rigor can mean stiffness and an inability to move.

Yikes!

I'm re-thinking this Academic Rigor idea...