More context is needed to fully understand this phrase, since this phrase could mean different things in different situations. However, this sounds like a line from a job description.
I would assume, in this case, that operational delivery means that the person is in charge of making sure that operations (which can often just mean the regular functions or normal work tasks of a person or group, often with the connotation of physical functions or work such as manufacturing or the running of a facility) are "delivered," or completed as planned and on time.
So, for example, if this is the job description of a Production Manager at a factory, that person would be responsible for making sure that all customer orders were manufactured efficiently, correctly and on time.
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