A rainbow table is "just" a big table of precomputed hash values with some trickery to store only a small portion of the table and still be able to lookup all values. In fine details, a rainbow table which can "invert" N possible values (i.e. there are N hash outputs for which the table will yield a corresponding input) takes time about 1.7*N to build -- so building the table is actually slower than "just" trying out the N inputs and see if one matches the given hash output. The table advantage is when you have several hash outputs for which you want to find a matching input.
