Milk is the first food, so dream tradition reads it as nurture, motherly care and the most basic needs. A full glass or jug of fresh milk speaks of abundance and of feeling looked after. Spilled milk is read as a small loss or a mistake that feels bigger than it is, and sour milk as care that has turned or a promise that went off. Giving milk to someone else points to your own role as the one who feeds and protects. It can help to notice who looks after you at the moment, and whether you let them.
Has this come up in your dreams before? What was going on in your life then?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.