What did i do wrong?

I don't if this is the place to post it.
But I can't figure this out.

elsif should be elseif

Also, you don't need the "== true" or "== false", you can just do:
if redstone.getInput("front")
and simply use an else statement (rather than elseif).

How will you make it with the else statement??. I'm not that good to cc..

Here, this script should give you the results you're looking for.

local mon = peripheral.wrap("back");
if mon then
  term.redirect(mon);
  print("Admin")
  print("is")
  if redstone.getInput("front") then
    print("OFFLINE")
  else
    print("ONLINE")
  end
end

Unfortunately, it isn't a very good one. If you're looking for something that'll react to the redstone signal as it changes, you'll want something like this:

local mon = peripheral.wrap("right");

function updateOnline()
    mon.setCursorPos(1, 3);

    if redstone.getInput("front") then
        mon.write("OFFLINE")
    else
        mon.write("ONLINE ")
    end
end

if mon then

    mon.setCursorPos(1, 1);
    mon.write("Admin");
    mon.setCursorPos(1, 2);
    mon.write("is")

    updateOnline();

    while true do
        local evt = os.pullEvent();

        if evt == "redstone" then
            updateOnline();
        end
    end
end

nothing is getting printet to the monitor when i do that program. :S

You mistyped part of it (you put "if more then" instead of "if mon then")

i did if more then. I did the if mon then. and it works. thanks. :(/>/>