Borrowing strength What are the principles of Borrowing Strength?
What does it mean in terms of estimating parameters for hierarchical models?
Where can this information can be read from?
 A: I am not certain this is the formal definition, nor the unique one, but the term was coined by John W. Tukey and often used in the context of empirical Bayes, or indeed, hierarchical models. 
It refers to the idea that assuming a distribution over your parameters of interest, information on one parameters, gives you information on other. Thus, each estimation "borrows strength" from others, via their assumed distribution.  
See here.
A: Here is an example. In the UK we are constantly told that violent crime rates are falling. We also hear reports of police adjusting data to make that case. The public are justifiably sceptical. However, data from hospital A&Es (Emergency Rooms) also shows a fall in hospital attendance because of violent crime. The crime data has borrowed strength from the hospital data to make it more credible. This is particularly compelling as the medical staff have no interest in the figures going one way or another.
This is a very important topic that gets too little attention. It has for me been a primarily judgmental thing (like exchangeability) rather than something that can usefully be modelled analytically.
