It means infant.Although the word "babe" for baby has been used since the 1300s, this phrase describing a child too young to walk (and hence having to be carried) dates only from about 1900.

eg: She's been a family friend since I was a babe in arms.

Note:

Babe in arms为还不会走路的婴儿，形容特别小、需要被抱着的孩子。Babe一词从十三世纪便开始使用，但是Babe in arms从十九世纪才开始流行。

例：从我还是个婴孩的时候，她就是我家的朋友。