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Parve (or parev in Yiddish) means food or dishes that are neither milchig (dairy) nor fleishig (meaty). They can therefore be eaten or used with either sort of food. Parve is especially used of foods you might expect to be milchig or fleishig, eg parve ice-cream.
From this, parve comes to mean lukewarm, wishy-washy, neither one thing nor the other; eg His speech was utterly parve; I felt parve about the last guy I went out with; He tries to be parve so that everyone will be his friend.
The etymology of parve is obscure. Balashon, a fascinating Jewish words blog gives the following suggestions; that parve is from the French word pareil, meaning similar; that it is the Latin parus, meaning equal, via Czech or Polish; that it is from the Latin parvus, meaning poor (food not enriched by butter or other fats); that it is a shortened version of the Spanish para toddas las veces, something that may be eaten at all times.
The explanation most plausible to me is that it comes from the Beit Haparve, a chamber in the Temple spoken about in Talmud tractate Yoma. The Beit Haparve, named after Persian builders and magicians of that name, was situated half in the area of the Cohanim and half in that of the Israelites hence the usage in kashrut.
One thing is clear; the more speculations there are about the origins of a word, the less likely is it that any of them is correct.