An approved ESTA does two things. It lets you board the plane to the United States, and it lets you arrive at a US port of entry. It does not let you enter the country. The decision on whether you actually get to step out of the airport is made by a Customs and Border Protection officer, after you have already flown.
For most travellers most of the time, this distinction is invisible. The CBP officer asks two or three questions, glances at the passport, stamps it, and you walk on. The questions become more pointed, and the distinction becomes more visible, when something in your file raises a flag.
What CBP officers look at, beyond the passport.
The officer can see your prior US travel record, your stated reason for travel from the I-94 system, and your declared length of stay. They are paid to spot mismatches between what's recorded and what you say at the booth. The ESTA itself is not in question; your intent is.
The three questions that matter.
“What's the purpose of your visit?”, “Where are you staying?”, and “When are you leaving?”. Be specific, be consistent with your ESTA application, and have the booking confirmations on your phone in case the officer wants to see them. Vagueness on any of the three is the most common cause of secondary inspection.
If you're referred to secondary.
It is uncomfortable but routine. Stay polite, answer questions briefly and factually, and do not volunteer information that wasn't asked for. Secondary inspection is not a refusal; it is a deeper check. Most travellers continue their journey within the hour.
Axis Visa is not a government organisation. Admission to the United States rests with CBP officers at the port of entry, not with Axis Visa or with the ESTA system.