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The expression comes from sequences. Given a sequence U1, U2, U3, ... the first differences are (U2 - U1), (U3 - U2), (U4 - U3) and so on.
If you consider these as the sequence V1, V2, v3, ... then the second differences in U are the first differences in V. So the second diffs are:
V2 - V1 = (U3 - U2) - (U2 - U1) = U3 - 2*U2 + U1
V3 - V2 = (U4 - U3) - (U3 - U2) = U4 - 2*U3 + U2, and so on.
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