A 3d printer bed is never actually flat, especially since 3d printers are cheaper and the tolerances are usually pretty loose compared to a super flat, precisely ground CNC bed for example.

One of the biggest issue/pain point in 3d printing for a while was to adjust the bed to make jt flat, or at least as flat as possible so that you can actually print without massive issues on the first layer. The process used to be manual, tedious and hit or miss (due to drift in the screws, or thermal expansion) etc.

Nowadays most new printers come with a sensor that probes the bed at multiple points (say in a grid of 4x4), then using for example a lagrange interpolation you can get a mesh that represents how flat your bed is. Then, using the visualisation you can either manually adjust the bed (with screws that rise or lower a certain corner), or even just let your printer compensate for the deviations.

That is, the printer moves the Z axis even when it is still printing on the same layer to make the print surface "virtually" flat (not always ideal if the Z axis stepper is trash, or if the deviation is too wide, or if there's too much vibration). That means that usually, the issue of bed levelling is mostly solved for newer printers!

Some printers also just use the nozzle itself as a probe, combined with a load cell. But those are usually on the higher end. The most common way is just a small probe of known size that sticks out and then calculates how much it extended before reaching the bed. (Some even use a pretty high res lidar to make sure the first layer is fine, even in some sub 900$ printers).

For a 3d printer the distance between the print bed and the nozzle when printing the first layer is very important. If the distance is too big the print doesn't stick to the bed and you end up with spaghetti. If the distance is too small either not enough plastic comes out so your print doesn't stick; no plastic at all comes out so your print doesn't stick; or the nozzle digs into the printbed, damaging it.

Since the thickness of layers in a 3d print is around 0.1-0.3mm the margin for error is rather tight. Since no one is going to invest in precision ground printbeds you need to get that precision by some other method. One of those methods is to probe the bed height at various points before printing, and driving the Z-axis to correct for that during the print.

The linked tool can be used to visualize how nonflat your printbed is given a set of such probes. The default example seems to have a ±0.25mm error, which isn't amazing but should be usable with mesh leveling and not at all without.

3D printers can do a variety of "bed mesh" leveling, which is where they probe the bed in a grid pattern and then can compensate for any deformities in the bed via software.

This ensures that the first layer (arguably the most important) for any print is perfectly flat and level. This visualizer takes the output of the bed mesh calibration sequence (where each point is a z-offset, usually from what the printer has defined as 0 based on the end stop) and graphs it so you can see your bed deformation.

Most Klipper frontend UIs already have support for this though

Some 3d printers have automatic bed leveling. Which is a process where the printer will touch the print bed in many places with a probe. This allows the printer to detect peaks and valleys, which it can then compensate for. The website above allows you to visualize that data.

Kinda neat to see a scaled up visualization of the vertical height differences of your printer bed.

https://marlinfw.org/docs/gcode/G029-ubl.html