DNA is a 2-stranded molecule. Each strand is essentially a string made up of letters {A,C,G,T}, and has an inherent direction. The two strands go in opposite directions, and have complementary letters (A opposite T, C opposite G). The reverse complement of a sequence is what appears on the opposite DNA strand; you get it by reversing the sequence and taking complementary letters.

So it's not a notion made-up by bored molecular biologists; it's really an inherent part of nature.

EXAMPLE

The first 60 letters of sequence AA000008 in GenBank are:
GGTTTATTTAGAGAATGACATGTGTACACTGTTAAGTGCTGATAGTGGATGCTGCAATTC
The reverse complement is:
GAATTGCAGCATCCACTATCAGCACTTAACAGTGTACACATGTCATTCTCTAAATAAACC

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