Income limits the deduction here, never the contribution
This is the distinction almost every page about traditional individual retirement accounts blurs, and it matters because getting it wrong stops people saving. Anybody with earned income may pay into a traditional IRA, at any income, up to the yearly allowance. What income can take away is the deduction — and it can only take that away if you or your spouse are covered by a retirement plan at work.
So there are really three situations. Nobody in the household is covered by a workplace plan: the contribution is fully deductible whatever you earn. You are covered and your income is inside the taper: part of it is deductible. You are covered and your income is above the taper: none of it is deductible, and the contribution is still allowed. In that last case the money goes in as after-tax basis, which you then have to track for the rest of the account's life, and which is the reason people in that position usually look at a Roth instead.
The page shows the deductible amount separately from the contribution for exactly this reason. A field that refused the contribution would be telling you something false.
How the taper works, and why it is not a cliff
Inside the range the allowance falls in proportion to how far through the range your income sits. Two small rules attach to it, and both are in the statute rather than in anybody's interpretation of it: the reduction is rounded down to the nearest ten dollars, which leaves you slightly better off than a straight proportion would, and the result never falls below two hundred dollars until it drops to nothing altogether at the top of the range. Without that second rule somebody near the top of the taper would be told they could deduct eleven dollars.
The range that applies to you depends on your filing status, and there is a fourth range that most tables omit: if you are not covered by a plan at work but your spouse is, a much higher range applies to you rather than the one your spouse gets.
The allowance is separate from the one at work
An IRA allowance is not shared with a workplace plan. Somebody contributing the maximum to a 401(k) may still pay the full IRA allowance on top of it. The two limits sit in different parts of the code and are adjusted separately, which is also why the IRA figure is so much smaller: it was never meant to be the main account for somebody who has a plan at work.
From the year you turn fifty the allowance rises by a catch-up amount. Unlike a workplace plan, there is no larger band in the early sixties — that one belongs to plans at work alone.
Paying in the maximum, year after year
The allowance is adjusted for the cost of living, so "the maximum" is a different number every few years. The form offers two ways to describe what you intend: hold the amount you typed, or raise it as the allowance rises. The second is what somebody who says they max out their IRA actually means, and it is the default, because holding a fixed figure for thirty years quietly assumes you will be contributing less and less in real terms.
What this does not do
It does not model tax on withdrawals, which is the whole other half of a traditional account: everything deducted on the way in, and all the growth on top of it, is taxed as income on the way out. It does not model required minimum distributions, which force money out of the account from a certain age whether you need it or not. It does not track after-tax basis, handle rollovers or conversions, or apply the penalty on withdrawals before the qualifying age. And it assumes one steady rate of return.