What is the meaning of ‘be obliged to’?

What is the meaning of ‘be obliged to’?

The passage below is from The Library: A Fragile History by Andrew Pettegree.

The library was a ubiquitous concept in rural Canada by the middle of the nineteenth century, but few libraries had staying power. In small communities, the survival of the local subscription library was often dependent on the energy of a few individuals. Anne Langton, who struggled to operate a library for settlers near Lake Sturgeon, Ontario, reflected in 1842 that ‘I think I shall be obliged to accept a pound of butter or a few eggs in payment [for the subscriber’s fee], and put the sixpence into the bag myself. I am afraid that I shall have to be perpetually dunning [chasing] one subscriber or another.’

I may come across this phrase hundreds, if not thousands, of times. But still I have to check out several dictionaries to look for exact meanings in a specific context, and sometimes however I may try, its meaning I cannot pinpoint. This paragraph is the very case I have come upon.

Let me tell you my guess for this context.

It says the woman’s despair for the hardship she has to endure running the library.

The sentence with underlined ‘be obliged to’ can be described as follows:

I think I have to do with meager payment of the subscriber’s fee. But since they also don’t have much money either, they pay partly in agricultural products such as a pound of butter or a few eggs and partly in small money like sixpence.

1. Do you agree with my paraphrsing?
2. In this paraphrse above I put the meaning of ‘be obliged to’ into ‘have to’. Am I right?

Thanks in advance.