Since this question doesn't specify that the quotes need to be related to any particular theme in Translations, I've included a variety of quotes that I think touch on important ideas and themes in the play.

• "Soon you'll be telling me all the secrets that have been in that head of yours all these years" (Manus to Sarah, act 1). In this quote, Manus suggests that Sarah, who is learning to speak, will be able to communicate all of the information stored inside her brain that she hasn't been able to communicate. This quote is an important one because it sets the stage for the importance of language in the play as a mechanism that "translates" the private realities of individuals into understandable signs. It's an idea that Friel returns to again and again, not only in Translations but in many of his other plays.
• "We name a thing and - bang! - it leaps into existence!" (Owen to Yolland, act 2, scene 1). Here, Owen gets over-excited at the prospect of translating the place names of Baile Beag into English. The suggestion is that naming a thing (or, in this instance, a place) results in a satisfactory definition of the imagined "essence" of that thing, thus communicating the deepest significance of the object or place that is named. Significantly, we should perhaps not take Owen and Yolland's efforts at naming very seriously, as they've been drinking throughout this scene and so are liable to exaggeration.
• "I will provide you with the available words and the available grammar. But will that help you to interpret between privacies? I have no idea. But it's all we have. I have no idea at all" (Hugh to Maire, act 3). In the closing moments of the play, Hugh promises to teach Maire English. However, Hugh also expresses doubts as to whether learning this new language will enable Maire to translate and understand the individual privacies referenced at the beginning of the play when Sarah speaks. It's a critical moment, as Friel illustrates his doubts about language's ability to interpret private realities. Some kind of important meaning, Friel seems to say, continues to elude us, even after we feel as if we've said everything we can possibly say.