Welcome. One way to find out what really makes the differences between one DMM and another is doing a thorough performance check:
electrical specifications: does it meet or exceed what's published in the manual?
ruggedness: can it take the abuse a portable device will, like being dropped to the floor?
ergonomics: is it easy to use
Dave gave a sample of those, but as the accuracy and features rise, the differences are very subtle and only a through test will reveal it, so its not immediately obvious what you spend all that extra money for. Its like getting any test gear, they look very similar up front until you push them to their limits.
Here's a sample. Its not easy to do without the right equipment and a lot more skill doing tests. I've been compiling this data over some weeks and its still incomplete. Here is a preliminary result comparing them to the HP 3456a, accurate to 1uV.
Blue line = Agilent 1252a, a $430 DMM 0.025% basic DC accuracy
Purple = Fluke 87V, a $300 DMM, 0.05% basic DC accuracy
Yellow = Sabtronics 2035a, a 1980s circa DMM that sold for $100, 0.5% basic DC accuracy
The curves on the left are from Vdc, stretching from 30mV to 1000V
The curves on the right are ohms, from single digit to megaohms
A simple explanation is the better meter should be as close to zero as possible, that's how far off its measurements are from the reference meter. What this preliminary data shows is that the Fluke 87V markedly understates its spec sheet in these tests, as its as accurate in DC and ohms, if not slightly better, that the more accurately rated Agilent 1252a.
The Agilent still has a valid calibration certificate, whereas the Fluke 87V has not been formally calibrated in 5 years.
The Sabtronics is still within it specification limits of 0.5%, but as you can see the cheaper meter has wide swings in percentage as it moves from scale to scale, whereas the expensive meters are much 'tighter' to the reference line.
What also has been completed but not shown is how the meters perform in ambient extremes of cold, heat and humidity. So you see, there can be much argument about whether a $50 meter is as good as $300 meter, but it won't be obvious until you do far more extensive tests than what Dave showed in his video.