What's in a name: bootstrapped replications? I am new to this material. I read this from a certain journal article. 
"The shaded region shows the 95% confidence intervals estimated from 1000 bootstrapped replications of the data."
My question is: What is being done when you do 'bootstrapped replications' of the data? Also, what is 'bootstrapping' in layman's terms, and why is it called as such?
 A: The bootstrap is done by taking your sample and resampling from it by sampling with replacement. Here is a small example.
Let's say you have a sample of 6 observations {$1,4,6,7,8,8.5$}.
A bootstrap sample is a sample obtained by sampling with replacement 6 times.  So a bootstrap sample could look like {$1,4,4,7,7,8.5$}. There are many possibilities. For each bootstrap sample, you get a sample estimate.  For a simple example let the estimate be for the mean of the distribution for the original sample that would be:
$(1+4+6+7+8+8.5)/6=34.5/6=5.75$
For the given bootstrap sample it is $(1+4+4+7+7+8.5)/6$=$31.5/6$=$5.25$.
Now there is a bootstrap distribution obtained by enumerating all possible distinct bootstrap samples and compute the estimate for each. But this is not usually done.  So we simulate taking bootstrap samples at random many times.
Each bootstrap is called a replication. In your case, you do 1000 replications.  That many replications are needed for good confidence interval estimation.
After taking the 1000 replications you have 1000 values for the sample mean (called the bootstrap distribution for the mean). From this sample take the appropriate percentiles of the bootstrap distribution to obtain the percentile method confidence interval.
For a 95% confidence interval you would take the 2.5th value from the bottom for the lower endpoint and the 97.5th value from the bottom to get the upper endpoint. Graphically you can make a histogram of the distribution and shade in the middle 95% of this distribution.
Efron named it bootstrap because it makes no special assumptions about the data other than iid. He thought of it as following the adage of picking yourself up by your bootstraps.
