A dainty little trinket or ornament.

Knick doesn't mean anything in itself in this term; it is merely a reduplication of knack. We now use knack as meaning 'a dexterous facility', but in the 16th century it was used to mean 'an ingenious contrivance; a toy or trinket', and that's the sense that was used in knick-knack.

John Heywood, used the word knack in his piece entitled The playe called the foure PP. A newe and a very mery enterlude of a palmer, a pardoner, a potycary, a pedler, 1540:

"Needles, thread, thimble, shears, and all such knacks."

Shakespeare also used it in The Taming of the Shrew, 1596:

"Why 'tis a cockle or a walnut-shell, A knacke, a toy, a tricke, a babies cap: Away with it."

When knick-knack was first used it meant 'a petty trick or subtefuge'. John Fletcher, used it that was in his work The loyall subject, 1618:

"If you use these knick-knacks, This fast and loose. "

By 1682, that meaning had died out though and a translation of Nicolas Boileau-Despréaux's Le Lutrin was using the term with the meaning we currently have for it, i.e. small trincket:

"Miss won't come in to Buy, before She spies the Knick-knacks at the Dore."