Thanks for reaching out and welcome to the community!
M/E stands for "mix effects". It is basically the main part of a production switcher that allows you to do things like cuts, cross dissolves, and overlay (also referred to as "keying" when any portion of an above layer is made transparent to reveal the lower layers) video or stills.
The full term is actually "mix/effects bus". The bus part refers to the two rows of buttons on the hardware control panel (preview buttons on bottom, program buttons on top). A single pair of preview and program buttons makes up one M/E.
For every M/E you also essentially get a "program" feed, which is the final video you see after all the cutting, cross dissolves, and keys are done. It's what you see on the final recording or live stream, for example.
So if you have a switcher that has multiple M/Es then you can have multiple program feeds for various things. One example of using multiple M/Es in a production is one feed used for a live stream and another feed used for in-house projection (also called IMAG). This allows you to have two separate "looks" happening at the same time from the same switcher.
You can also mix downstream M/Es (higher numbers) with upstream M/Es (lower numbers). So, for example, you can show M/E 2 on M/E 1 just like you would another source, like a camera or graphic.
Can you describe your situation and needs in a little more detail? Is this for a church or another type of situation? How many cameras (or total inputs) do you need to start with? Do you need the ability to have multiple feeds at the same time, like streaming and IMAG?