I understand the meaning of the word almighty, but what does the phrase almighty dollar mean?
This is a contemptuous phrase. It means that money is a bit like a deity. So the term almighty dollar is used to refer to the power of money.
Almighty means absolute or supreme.
Hinduism was the first religion to teach the existence of a supreme deity having almighty power.
Almighty is almost never, informal usage, applied to anything other than the attributes of God Almighty. In slang, however, the word is commonplace, as in the sentence she’s almighty proud, meaning extremely or excessively proud. Then, of course, there is the contemptuous phrase the almighty dollar.