The verse appears as follows in the Greek New Testament:
Luke 1:37 (mGNT)
37 ὅτι οὐκ ἀδυνατήσει παρὰ τῷ θεῷ πᾶν ῥῆμα.
The best literal translation would be as follows:
Luke 1:37 (ASV)
37 For no word from God shall be void of power.
The Word of God is therefore inviolable, or incapable of non-fulfillment. When the Lord speaks His word(s), the result must occur, because any word He speaks is inviolable, or incapable of non-fulfillment.
Ezekiel 12:25 (NASB)
25 For I the Lord will speak, and whatever word I speak will be performed.
Thus some New Testament translators have relied on the more colloquial, nothing is impossible for God (or variants of the same phrase), since the Lord need only speak the word in order to effect any outcome in accordance with His own will. In the context of the Luke passage, the miracle of the incarnation was based on the word spoken from the Lord and transmitted to Mary by the angel Gabriel (Luke 1:38). Thus the "word" became flesh.