Rounding answers one plain question: which round number is this closest to? That's it. The "round numbers" might be the nearest whole, or the nearest tenth, or the nearest hundredth — but the question never changes.
It's a Number Line, Really
Picture 3.4 sitting on a number line. The two nearest whole numbers are 3 and 4. Is 3.4 closer to 3 or to 4? It's only 0.4 above 3 but 0.6 below 4 — so it's nearer 3, and we say 3.4 rounds to 3. Drag the point in the toy and you'll see the two nearest marks light up, with the closer one called the winner. Rounding is just naming the nearest marker.
Why "to a Given Accuracy"
The "given accuracy" just tells you how fine the marks are. Round 2.83 to the nearest whole and the marks are 2 and 3 (answer: 3). Round the same number to the nearest tenth and the marks are 2.8 and 2.9 (answer: 2.8). In the toy, press "zoom to tenths" and the marks get ten times closer together — you're now snapping to a much finer grid. Same number, different accuracy, different answer.
So Why Bother at All?
Because real measurements are messy. A tape measure might read 3.4187 metres, but nobody needs all that — "about 3.4 m" is honest and useful. Rounding is how we report a number to a sensible level of detail without pretending we measured more precisely than we did.