In what way is the labor participation rate useful for tracking unemployment? I'm trying to do some research on unemployment and labor participation rate in the US to figure out what people are talking about.

For instance, the Civilian Labor Force Participation Rate for Sept 2016 is 62.9% (FRED 1). My attempt to control for retirement would be to look at the 25-54 age group series, which puts the labor participation rate at 81.7% (18.3% unparticipation) (FRED 2), but I'm guessing there a number of things wrong with that approach. The Bureau of Labor Statistics says the U-6 unemployment is 


  Total unemployed, plus all persons marginally attached to the labor force, plus total employed part time for economic reasons, as a percent of the civilian labor force plus all persons marginally attached to the labor force


and gives the Oct 2016 number as 9.5% (BLS 1). This sounds like an all-inclusive definition, or what people "really" mean when they talk about unemployment, but that differs from the 25-54 labor participation rate by quite a bit (9.5% vs 18.3%).

Question

In what way is the labor participation rate useful for tracking unemployment? It seems there are a large number of people included in labor participation that shouldn't be included when trying to measure unemployment, for example, the number of people retired and choosing not to work.

(side question: is there a number of people retired series on FRED? I'm not seeing one...)
There's a very fine point that needs to be mentioned: 

The participation rate is the percentage of adult population of a country that is capable of work and wanting to work, individuals who are capable and wanting to work are the labor force. 

Now when unemployment is measured, it is typically the percentage of individuals in the labor force who actually have the kind of employment (in terms of time worked) that they desire. 

The importance of the participation rate is the following: when some individuals are unemployed for a long period of time, they eventually stop looking for work (the "willing to work" part is no longer valid) either because they've given up, or their skills are too outdated to be useful to the market. These individuals are dropped out of the labor force. 

Assuming all else is constant, these unemployed individuals leaving the labor force means there are less unemployed individuals as a percentage of the total labor force (lower unemployment rate), but now the participation rate is lower (smaller labor force divided by same total adult population).

Therefore, unemployment numbers aren't really telling you the whole story if you assume that people dropping out of the labor force would actually want to work if they had found work, and thus unemployment rates alone may give a better picture of how workers are actually doing.

In short: 

Unemployment rate = total employed/ labor force

Participation rate = labor force/adult population

As for the retired, I believe those are considered outside the labor force.

Example:

Assume a coal miner has no other job market skills than the ability to mine coal. Assume country X bans coal mining. All coal miners are left without a job but will not search for a job because they can't do any other job. The unemployment rate is unchanged, but the participation rate drops.

Very generally:


Unemployment rate rising, participation rate rising => not creating new jobs fast enough to absorb growth in labor force
Unemployment rate rising, participation rate falling => long term recession
Unemployment rate falling, participation rate falling => people are leaving the labor force
Unemployment rate falling, participation rate rising => high job creation