The second number reflects the difficulty of the [hardest part of the] climb. I believe it originally went from 1-10, with 10 being the hardest thing a human could climb, but innovations in climbing shoes and better climbers have raised the max over the years, so now it goes from 1-15.
Imagine the scale as being of exponential difficulty. For the same climber who spent a week going from 5.5 to 5.6, it may take a year to go from 5.10 to 5.11. So you can imagine how elite a 5.14 climber is, let alone a 5.15 one.
http://en.wikipedia.org/wiki/Grade_%28climbing%29#Free_climb...
http://en.wikipedia.org/wiki/Yosemite_Decimal_System#YDS_cla...
The difficulty is rated as one pitch relative to another and certain pitches as benchmarks for a certain difficulty. e.g. pitch X is 5.13a and pitch Y is somewhat harder so it's 5.13c while Z is quite a bit harder making it a 5.14a, etc.
5.6 can be climbed by any healthy adult, 5.7 by most. I reached 5.11 in a year of climbing; I expect to reach 5.12 within 5 years, and 5.13 sometime within my lifespan if I am dedicated and train relentlessly. 5.14 is only within reach of the greats who live their lives to climb, and 5.15 has been climbed by 2-3 people on this Earth.
More people will climb 5.14 & 5.15 in the future, but the progress of peak potential is slowing.