No-dig gardening is exactly what it sounds like: instead of turning over or tilling the ground before planting, you build layers of compost and other organic matter directly on top of it and grow into that instead. It's a genuine shift from the traditional dig-it-over approach most beginner gardening advice still assumes, and it's become popular in New Zealand home gardens largely because it's less physical work as well as being better for soil health.
The usual starting point is a base layer of cardboard or several sheets of newspaper laid directly over grass or weeds. This smothers what's growing underneath by blocking light, so it dies back and breaks down in place rather than needing to be dug out first. On top of that base layer goes a generous depth of compost, well-rotted manure or other organic matter, deep enough to plant straight into without disturbing the smothered layer below. There's no need to remove turf or work anything into the existing ground at all.
The reasoning behind skipping the digging step comes down to what's already living in undisturbed soil. Digging or tilling physically breaks apart soil structure and disrupts the fungal networks and microorganisms that build it back up naturally, the same organisms responsible for much of a healthy soil's ability to hold water, cycle nutrients and support root growth. Leave that structure alone and it keeps doing that work; dig it over repeatedly and you're constantly setting it back to square one.
Digging or tilling physically breaks apart soil structure and disrupts the fungal networks and microorganisms that build it back up naturally
In practice, this means you plant directly into the compost layer on top rather than into the original soil underneath. Roots from most vegetables establish perfectly well in a good depth of compost, and as the compost breaks down further and the smothered layer beneath it decomposes, the two gradually merge into improved soil over time, all without a spade ever going into the ground.
No-dig isn't a replacement for feeding your soil well; it still relies on a genuinely good depth and quality of compost to work, which is worth reading up on separately if you're building your first bed. What it changes is the method, not the need for organic matter, and for many home gardeners it turns bed preparation from the heaviest job in the garden into one of the lighter ones.