Cause:  

Usually because the root grew too quickly for its outer tissue to keep up. The classic cause is  uneven soil moisture,  particularly a dry period followed by lots of rain or heavy watering. The carrot suddenly takes up water and expands, and the root splits.  

Leaving mature carrots in the ground too long can make cracking more likely, and some varieties are more prone to it than others.

How to Fix It

Once cracked there's no going back.  Prevention is the key.  Keep soil moisture as even as possible, especially as the roots size up. Mulch helps reduce rapid swings between wet and dry soil. Water deeply and consistently rather than allowing the bed to become very dry and then soaking it. Harvest mature carrots rather than leaving them indefinitely in the ground.

Avoid excess nitrogen, which can encourage rapid growth. Unless you have a known nutrient deficiency, cracking is primarily a water management problem.