What could happen if we didn't activate plane mode in planes?

As far as I know, your phone will continue trying to connect to any cell tower nearby, and potentially interfere with airplane's communications with ground control. I don't think a single cell-phone will cause so many problems, but if all the cell-phones are still on, the risk will be compounded. That's why, as a rule, we turn on airplane mode.

What do you mean by "activate plane mode"?