It's a very dynamic relationship in that the two change each other and the effect can differ over the short and long term.
The participation rate refers to the total percentage of the population which are either employed or unemployed as a percentage of working age population (I believe it's 15 until retirement age).
When the participation rate goes up more people are looking for work and hence in the short term it is likely unemployment (percentage of labour force looking for work but not currently employed) will go up as more people will be looking for work and jobs available may not keep up. In the long term however in the labour market a high participation rate usually means the supply curve for labour resources has shifted to the right, meaning labour is cheaper, hence unemployment will go down as labour will be cheaper, allowing businesses to buy more labour.
A high unemployment rate may reduce the participation rate due to hidden unemployment, as people can't find jobs and give up looking when there is high unemployment, hence they leave to labour force and the labour force as a percentage of the working age population decreases, hence the participation rate falls. If the unemployment rate begins to fall the opposite is likely to occur with the participation rate increasing as these previous discouraged jobseekers reenter the labour market searching for work.
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