stone resembling jade
珉 refers to a type of stone that looks like jade but is not true jade. Its meaning is narrow and concrete: a jade-like stone.
珉 combines 王 (jade/jewel) with 民, which likely contributes the sound. The character denotes a stone similar to jade.
The left side 王 (jewel) tells you it's a gem-like stone, and the right side 民 (people) suggests it's a common stone that ordinary people might mistake for jade.
For ビン, imagine a bin full of stones that look like jade: bin -> ビン, and you pick one out to examine.