In using a cloning vector with a multiple cloning site spliced into the front part of the lacZ gene, production of beta-galactosidase, as shown by the blue color when grown on Xgal, indicates that:

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When a cloning vector with a multiple cloning site spliced into the lacZ gene is used, the production of beta-galactosidase (indicated by blue color on X-gal) means that the lacZ gene is intact and functional, which happens when there is no insert in the multiple cloning site. If an insert were present, it would disrupt the lacZ gene, preventing the production of beta-galactosidase and resulting in white colonies instead of blue.

In Using a Cloning Vector with a Multiple Cloning Site