Translation:January is the first month of the year, and February the second.
I wonder whether Zamenholf was aware of how months were named in East Asia. January is literally "month one", February is "month two", and it goes all the way up to "month 12". He could have named January "Unmonato", February "Dumonato", etc., rather than have their names derived from the Romance languages.
And, going back to the ancient Roman roots of the current Gregorian calendar, September, October, November and December were the 7th (Sept), 8th (Oct), 9th (Nov) and 10th (Dec) months of the year. Then the Caesars added July (Julius) and August (Augustus) and those months no longer had their numerical place in the year.
It's called ellipsis. When two sentences are joined like that and have otherwise parallel construction, key words in the second part can be omitted because they're understood to be the same as in the first part.
January is the first month of the year, and February [is] the second [month [of the year]].