What's the meaning of the phrase 'Shilly-shally'?
To 'shilly-shally' is to be indecisive and vacillating.
It seems to make sense that 'shilly-shally' is just a variant of 'dilly-dally'. The two expressions are almost identical and mean much the same thing. However, that isn't the case. Although 'shilly-shally' is the later phrase in origin it was coined independently from dilly-dally'.
'Shilly-shally' is a colloquial way of saying 'Shall I? Shall I not?' and, as such, has more in common with the earlier expression willy-nilly (Will I? Will I not?).
Almost all of these 'this way or that way' expressions follow 'this' and 'that' in their construction. That is, the second word replaces the 'i' of the first word with an 'a'. Examples are, dilly-dally, wishy-washy, chit-chat, zig-zag.
What's the origin of the phrase 'Shilly-shally'?
Many of the early examples of 'shilly-shally' in print are in the form 'to stand shill I, shall I'. This emphasises the vacillation conveyed by the phrase.
The earliest use of shilly-shally' in print that I know of is in the narrative poem Loves Victory Obtained, published in London in 1655, in which a young woman encourages a suitor:
Prethee sweet-heart do not dally,
nor delay no time with me,
Stand not fooling shilly, shally,
but be courteous and agree:
Note that 'to agree' in 17th century England meant 'to consent to be romantic partners'.