text is not a function in your case. Just have it as:

value = 'ButtonA'
btna = Button(root, text = value, command = lambda: sayHi(value))

And you will get that working.

This can also be done by using partial from the standard library functools, like this:

from functools import partial
#(...)
action_with_arg = partial(action, arg)
button = Tk.Button(master=frame, text='press', command=action_with_arg)

Sorry for being 6 years late, but recently I figured out a good way to do this without making your code messy and hard to maintain. This is pretty much what DaveTheScientist has said, but I just want to expand on it a little. Usually, in Tkinter, if you want to have a button call a function, you do the following:

exampleButton = Button(root, text = 'Example', command = someFunc)

This will simply call someFunc whenever the button is pressed. If this function, however, takes arguments, you need to use lambdas and do something like this:

exampleButton = Button(root, text = 'Example', command = lambda: someFunc(arg1, arg2))

The above line of code will run someFunc and use the variables arg1 and arg2 as arguments for that function. Now, what you could do in a program where, a lot of the times, you would need the functions run by buttons to return values, is create a new function which is called by every button.

This function takes the function you want your button to run as a first argument, and that function's arguments afterwards.

def buttonpress(function, *args):
    value = function(*args)

Then when you create the button, you do:

exampleButton = Button(root, text = 'Example', command = lambda: buttonpress( someFunc, arg1, arg2 ))

This will run the given function (in this case, someFunc) and store the returned value in the value variable. It also has the advantage that you can use as many arguments as you want for the function your button runs.

Your second attempt was close, but since checkPassword isn't a class method, you shouldn't be prefixing it with self..

def checkPassword(event, some_value_you_want):
    # do stuff

Entry.bind("<KeyRelease-Return>", lambda event: checkPassword(event, name_of_your_entry_widget))

What about

import functools
def callback(self, event, param):
    pass
arg = 123
widget.bind("", functools.partial(callback, param=arg))