To whittle is to pare or carve away. Wood carvers whittle pieces of wood, removing bit by bit until what's left is a sailor with a yellow raincoat or a lone wolf howling at the moon.
Whittle can also mean to reduce an amount or number of items. In this sense, it is commonly paired with the words away or down. A courtroom attorney might "whittle away" at a defendant's alibi until the truth emerges. You might "whittle down" a to-do list or "whittle away" at your student loan debt every month. But only a highly skilled wood carver can whittle a chunk of pine into that old salty dog with a yellow raincoat.