I'll try a "short" answer.
Cortex is the result of a new naming convention from ARM. In the past ARM has numbered their cores, ARM7 very successful, ARM8 a flop, ARM9 very successful, ARM10 a flop, ARM11 very successful, and what now?
Call it ARM12 and prepare for another flop? Call it ARM13 and have all the superstitious people go bananas? They had a problem.
Now some wise guys came up with the idea to call ALL future cores from ARM Cortex and a suffix.
There is Cortex-A for applications processor, the high end running > 1 GHz
There is Cortex-R for real-time processor, the mid range 400-600 MHz
There is Cortex-M for microcontroller the low end running < 200 MHz
Watch closely Cortex-A-R-M spells ARM again
With Cortex, new devices have an extended instruction set, most important Thumb2. All Cortex devices support the more efficient Thumb2, smaller code and a mix of 16/32-bit instructions.
For a list of many Cortex-M based devices and articles check out this site:
**broken link removed**
Other important improvements of Cortex-M over ARM7
Faster and more predictable interrupts
Better debugging support
Lower power
More performance at the same clock speed
and many more
hope this helps, Bob