Hydro-erosive grinding is a way of shaping or smoothing a material using water and a powerful jet of tiny particles. Imagine that you have a sandcastle on the beach and you want to smooth it out using a hose with a really strong shower head. When you turn on the hose and point it at the sandcastle, the water comes out in a big stream and hits the sand very hard. This makes the sand move and wear away. That's kind of like what hydro-erosive grinding is, but on a much bigger and more precise scale.
In hydro-erosive grinding, instead of a hose with a shower head, they use a machine that shoots a tiny jet of water at a really high speed. This water jet is mixed with tiny particles that are harder than the material being ground (kind of like sandpaper, but much smaller). When the water and particles hit the material, they wear it away and shape it into whatever the designer wants.
This process is used for a lot of different things. For example, it can be used to make precise cuts in metal parts for machines, or to shape glass for lenses in eyeglasses or cameras. The water and particles used in hydro-erosive grinding are so powerful that they can even cut through steel and other super-strong materials that would be very difficult to cut with other methods.