What is "Manuscript Evidence" and how is it useful?

In several Apologetics articles (including one answer of mine on a different question), I see the statement that "there is overwhelming manuscript evidence to support the fact that the Bible has been transmitted accurately through time". Often, these sites contain a chart like the following, with no explanation of why the number of copies, or the gap between the original written version and the earliest known manuscript matters. So how does all of this prove anything? Does it prove the Bible is the Word of God? If not, what's the point?