。
Please don't cry.
Literal
Favor [copula-だ-reason-から] cry-not [request-で].
お願いだから literally 'because it is a favor/request' — a set phrase used as a pleading preface to a request, softening and emotionally charging what follows. 泣かないで is the casual negative request (~ないで form). Together they form a sincere, vulnerable plea rather than a neutral request.