What does "humble" mean?

America has spoken, and I'm humbled by the trust and the confidence of my fellow citizens. With that trust comes a duty to serve all Americans, and I will do my best to fulfill that duty every day as your President.
Hi Jobb,
It means 'to make (someone) humble'.
The adjective 'humble' means to have a low opinion of your own importance.

eg The blue team beat the green team by a very big score, so 'the blue team humbled the green team'.

But ... many people do not see George Bush as a humble guy in any way! Have a look at the word 'arrogant'.

Hello Jobb

'Humble' etymologically means 'low', 'near the ground'.

If a person is 'humble', he is either (1) 'modest; conscious of his shortcomings and insignificance', or (2) 'of low status'.

If an object is 'humble', it is either (3) 'simple and plain', or (4) 'of the kind
that would belong to a person of low status'.

'Humbled' comes from the verb 'to humble'. This verb can mean either 'to
cause to become humble' in sense (1), e.g. 'I feel humbled by this honour',
or 'to humiliate', e.g. 'Napoleon's armies humbled the kings of Europe'.

So in your extract, the speaker is rhetorically claiming that the trust and
confidence of his fellow citizens have made him 'humble' in sense (1).

It used to be common to end letters like this:

Your humble servant,

In the phrase 'in my humble opinion' ('IMHO'), 'humble' is also used in sense
(1), and is transferred from the speaker - i.e. the speaker is conscious of his own
shortcomings, and so offers his opinion tentatively.
Sorry, Clive, I didn't see you'd already answered.
Students: We have free audio pronunciation exercises.
Also thank Clive, at least he inspired me, too.
Students: Are you brave enough to let our tutors analyse your pronunciation?