Cyril of Alexandria gives this interpretation:
They replied, that they had been labouring the whole night, and had caught nothing: in the name, however, of Christ, they let down the net, and immediately it was full of fish; in order that by a visible fact... they might be fully convinced that their labour would not be unrewarded, nor the zeal fruitless which they displayed in spreading out the net of the Gospel teaching; for that most certainly they should catch within it the shoals of the heathen.
The apostles, as "fishers of men," preached the good news to "the lost sheep of the house of Israel," achieving not enough success to allow Jesus to be widely recognized. In allegorical terms, they stayed close to the shore. In future times they would "fish" in deeper waters, meaning both among Jews beyond their region of origin (the Galilee) and eventually including people of other religions and nationalities. There they would indeed find great success. Luke focuses on this theme in his sequel work, the Book of Acts, where the Gospel indeed spreads with great success among the Samaritans and the Gentiles.
St. Ambrose thinks the "duc in altum" ("launch out into the deep") means to launch
in profundum disputationum
John Henry Newman transl. of St. Thomas's Catena Aurea: "into deep researches".
Ni Riain transl. (p. 115): "into the deep waters of controversy".
Although the Lord commands others to let down the nets, it is only to Peter that He says: “Launch out into the deep” (Lk 5:4). By this He means, launch out into the deep waters of controversy. No depth can be compared to the sight of the profundity of the riches (cf. Rom 11:33) of the knowledge of God's Son, and the proclamation of His divine nature. Of course, the human mind cannot grasp this mystery nor can human intelligence plumb its depths. Faith alone, Faith in all its fullness, can embrace it. For even though it is not right that I should know in what manner He was born, it is also not right that I should fail to know that He was born. The “how” of His Birth I do not know, but I recognise that fact that He was generated by His Father. We were not there when the Son of God was born of the Father; but we were there when the Father proclaimed Him Son of God (cf. Lk 3:22).
It's also interesting to note that it is darker in the "deep", so perhaps Jesus is saying that more converts will be made of the gentiles who are farther from the Light than of those (e.g., Jews) in shallow waters closer to It; "many are the children of the desolate, more than of her that hath a husband" (Is. 54:1).