Very interesting. I found this explanation on geneology.about.com:
In earlier times, a marriage bond was given to the court by the
intended groom prior to his marriage. It affirmed that there was no
moral or legal reason why the couple could not be married and it also
affirmed that the groom would not change his mind. If he did, and did
not marry the intended bride, he would forfeit the bond. The bondsman,
or surety, was often a brother or uncle to the bride, not necessarily
a parent. The bondsman could also be related to the groom, or even be
a neighbor or friend, but those situations occurred less often.
There was also this longer bit I found by Richard A. Pence that goes into the history better:
A bit of history may help us to understand the nature of the marriage
bond. In early colonial America, "marriage banns" were usually the
formal process leading up to the wedding. Notice of the impending
marriage was read from the church pulpit or posted at the church door
over a set period of time. The purpose of this was to allow those who
knew the bride and groom to object if there was a legal reason why the
marriage should not take place ("speak now or forever hold your
peace").
There were three principal legal barriers: either or both were not yet
of legal age, either or both were already married, or the bride and
groom were too closely related to marry under the laws of the
jurisdiction.
As America gradually became more of a frontier nation, often either
the bride or the groom would not be well known in the community. To
overcome this, the marriage bond soon replace the banns.
The groom and a suitable bondsman ("surety") would pledge an amount
(usually specified by law) to an official (often the governor of the
colony or state) as a guarantee that there were no legal impediments
to the forthcoming marriage. The bond was "conditional" -- that is,
the pledged amount would be forfeited only if there proved to be a
legal reason the couple should not marry. If no such legal barrier
existed, the bond would be null and void, even if the wedding failed
to take place for some other reason. In many jurisdictions the bond
remained in force for a year or two after the marriage and apparently
would have been forfeited if any illegality came to light during that
time.
Use of the marriage bond began to fade in the middle to late 1800s and
by the close of the century most jurisdiction relied on "sworn"
statements made in the application for the marriage license to guard
against illegal marriages.
The thing I find interesting about this is the implication that bonds were used when records about things weren't all computerized and networked, and the people in question weren't well-known enough in the community for the legality of the marraige to be "crowd-sourced" to the community at large.
This bit of crowd-sourcing lives on in our traditional marriage cerimonies, in that the minisiter usually asks "Before we proceed, if anyone here knows any reason why these two should not be married, speak now or forever hold your peace.", and then pauses waiting for a response from the crowd.
What this implies about your particular ancestor in London is either that either he and/or the bride were not well-known in their area, or that perhaps in a huge city like London nobody could be well-known enough for a bann to be effective.