Global - local variables

[buran]

you need to declare it global.

Flag = 0
nuserySWdatabase = 0 # this would be from database but is set to 0 for testing
 
def nuseryControlFunction(nuserySWdatabase):
    global Flag
    if ( nuserySWdatabase == 0 and Flag == 0):
        print ("pump on")
        Flag = 1
        print Flag
    else:
        print ("pump off")
        Flag = 0
 
while 1:
    nuseryControlFunction(nuserySWdatabase)
    print Flag

Yet way way better would for your function to return the flag. If you don't change it inside the function, you can access flag from global scope.

nuserySWdatabase = 0 # this would be from database but is set to 0 for testing
flag = False
def nuseryControlFunction(nuserySWdatabase):
    if nuserySWdatabase == 0 and not flag:
        print("pump on")
        return True
    else:
        print("pump off")
        return False
 
while True:
    flag = nuseryControlFunction(nuserySWdatabase)
    print(flag)

But still better would be to if your function has flag as second parameter (if you need it at all - from your code I cannot decide if it really needed).

nuserySWdatabase = 0 # this would be from database but is set to 0 for testing
flag = False
def nuseryControlFunction(nuserySWdatabase, flag):
    if nuserySWdatabase == 0 and not flag:
        print("pump on")
        return True
    else:
        print("pump off")
        return False
 
while True:
    flag = nuseryControlFunction(nuserySWdatabase, flag)
    print(flag)

Also, note your names do not comply with PEP8 recommendations but I kept them