An HSA is a type of financial account somewhat similar to an IRA, that is, it is owned by you (and not by your employer) and persists from year to year (not like an FSA).
HDHP (High Deductible Health Plan) is a health insurance policy similar to your regular employer provided health policy, except it meets certain IRS requirements, which enable you to contribute to an HSA.
"Company is telling me that number is what we paid toward our insurance" No, the amount that your company pays for the HDHP premiums should be reported with code DD in box 12 of your W-2.
As Julie noted, the code W amount is the amount that your company contributed to your HSA (if anything) plus whatever you contributed by payroll deduction (if anything).
It is clear that your employer needs to speak to a tax professional or a payroll processing professional (who should understand this), because as it stands, you need to get a corrected W-2.
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