Let's break it down:
* ab irato origine: "from the angry origin" (referring to the anger of Romulus and Remus's grandfather, Numitor)
* ob ovo usque ad mala: "from the egg to the apples" (referring to the beginning and end of a traditional Roman meal)
* uno disce omnes: "learn all from one" (meaning learn all of Roman history from one source)
* urbe condita utili: "from the founding of the city [Rome] useful"
This phrase is a playful and memorable way to summarize the "Ab Urbe Condita" (From the Founding of the City), a monumental historical work by the Roman historian Livy. It essentially means: "From the angry origins of Rome, to the end of a Roman feast, learn all of Roman history in one useful book."