It means that someone has agreed to pay a certain amount of money, and they can't go back on it. e.g. If I say "I pledged to pay the charity $500," it means the same thing as if I said "I promised to pay the charity $500."
BUT! Also note that "pledge" can also mean to show respect for something. e.g. to pledge allegiance to a flag This is an important thing to know, because almost all schoolchildren in the US know this expression from reciting the "pledge of allegiance" to the US flag every morning ("I pledge allegiance to the flag of the United States of America, and to the republic for which it stands...").
I wasn't exactly sure how to explain what 'pledge of allegiance' meant, but I agree more with your explanation. :) Just wanted to bring that up as it's one of those cultural things no one thinks to tell you.
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