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Greenleafable
A prepositional phrase, as the name itself suggests, has to do with prepositions. So it is a phrase which starts with a preposition, and includes one, or more words after it. 
In this case, the prepositional phrase is of dried meat, vegetables, and flour. The phrase acts as an adjective - what kind of supplies? (Those) of dried meat...
Kalahira
The prepositional phrase is "their supplies of". From the sentence we know what was being rationed, the supplies. The phrase "their supplies of" is a preposition that enables to sentence to contain the items contained therein - dried meat, vegetables, and flour.

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