In the biblical episode, several wealthy temple patrons donate large sums of money, while a poor widow places just two small coins into the offering.
She finds greater favour with Jesus than the wealthy patrons however, as the two coins constitute her whole wealth, as opposed to a tiny fraction from the rich merchants of theirs.
There is also some belief that the idiom may have its origins in the early cost of postage in England, the "twopenny post", where two pennies were the normal charge of sending a letter containing one's words and thoughts or feelings to someone.
By deprecating the opinion to follow—suggesting its value is only two cents, a very small amount—the user of the phrase, showing politeness and humility, hopes to lessen the impact of a possibly contentious statement.
For example: "Federal Opposition spokesperson Bob Hawke threw in his two-bobs' worth when he opened the Ironworkers national conference this week".