Bootstrap analysis, bootstrapping etc are quite common jargons of bioinformatics and phylogenetics. However, it is not very much clear to us, what exactly being meant by a boot's straps. Does it means a comparison? (Such as we hold the two straps of a boot (shoe) in two hands; may be an analogy to comparing 2 things (say left-'hand' side and right-'hand' side of an algebraic proof-task)) or it is something about sequence alignment (since we 'tie' a knot in boot (shoe) so that the 2 ends of the strap remain attached to each-other). Some of my classmates even assumed it may be a process during computer booting (but I could not agree with that). I've searched internet, but could not found anything very helpful. This wikipedia page (permalink) about bootstrapping, tells,  Tall boots may have a tab, loop or handle at the top known as a bootstrap, allowing one to use fingers or a boot hook tool to help pulling the boots on. The saying to pull oneself up by one's bootstraps was already in use during the 19th century as an example of an impossible task. The idiom dates at least to 1834, when it appeared in the Workingman's Advocate: It is conjectured that Mr. Murphee will now be enabled to hand himself over the Cumberland river or a barn yard fence by the straps of his boots. In 1860 it appeared in a comment on philosophy of mind: The attempt of the mind to analyze itself an effort analogous to one who would lift himself by his own bootstraps.  Bootstrap as a metaphor, meaning to better oneself by one's own unaided efforts, was in use in 1922. This metaphor spawned additional metaphors for a series of self-sustaining processes that proceed without external help. The term is sometimes attributed to a story in Rudolf Erich Raspe's The Surprising Adventures of Baron Munchausen, but in that story Baron Munchausen pulls himself (and his horse) out of a swamp by his hair (specifically, his pigtail), not by his bootstraps  and no explicit reference to bootstraps has been found elsewhere in the various versions of the Munchausen tales.(In the quotation, highlighted portion seemed to tried to tell a meaning), but it wasn't also very much helpful. Could not correlate with bioinformatics. (Btw the same wikipedia article mentions computer booting). Wikipedia article about Bootstrapping (statistics) (permalink) tells: The bootstrap was published by Bradley Efron in Bootstrap methods: another look at the jackknife (1979), inspired by earlier work on the jackknife.Improved estimates of the variance were developed later. A Bayesian extension was developed in 1981. The bias-corrected and accelerated (BCa) bootstrap was developed by Efron in 1987, and the ABC procedure in 1992. Still that is not very helpful. However, the textbook, Introduction to Bioinformatics/ Arthur M. Lesk/ 3rd Edition/ Oxford / (Low Price edition) ; in its chapter 5 (Alignments and phylogenetic trees), section The problem of varying rates of evolution -> computational consideration (page 296); a clearer definition has been given: Formal statistical tests, involving rerunning the calculation on subsets of the original data, are known as jackknifing and bootstrapping.         jackknifing is calculation with data sets sampled randomly from the original data. For phylogeny calculations from from multiple sequence alignments, select different subsets of the position in the alignment, and rerun the calculation. Finding that each subset gives the same phylogenetic tree lends it credibility. If each subset gives a different tree, none of them are trustworthy. Bootstrapping is  similar to jackknifing except that the position chosen at random may include multiple copies of the same position, to form data sets of the same size as original, to preserve statistical properties of data sampling. More clear definition of Boot-strapping; but it does not explain, where the relation exists with the boot (shoe) and its straps. 
Bootstrap analysis - why it is called bootstrap?
terminology;bootstrap analysis
The method itself has nothing really to do with boots or straps, just as the jack-knife method also has nothing to do with knives. In the case of bootstrapping, the goal is to determine the accuracy of an estimate from random subsets of a population. Normally estimating something like the variance of the mean requires multiple independent samples, but bootstrapping allows you to perform estimates from a single population. This is essentially allowing the estimate to pull itself up by its bootstraps, which is the only reasonable source for the term. See also the more general wikipedia article on bootstrapping outside of statistics.