To do something plainly means to do it either in a very simple way or in an obvious way. You might dress plainly when you're just hanging around the house, but your flair for fashion will be plainly visible when you get dressed up for a party.
If you're plainly asking your mom for money, it's clear to her what you're doing. But if you live plainly, it means you do things in a simple, non-luxurious way. You can also speak plainly, which either means "using simple words," or "bluntly." Certain religious groups, including Quakers, Amish, and Mennonites, have long been associated with the words plain and plainly because they live, speak, and dress so simply.