I can only suggest you read a book on C or C++, however as far as your code goes:
int blinkmodeon = 1; // sets blinkmodeon to the integer value 1
while (blinkmodeon == '1') // compares blinkmodeon to the character '1', i.e. the byte value 0x49
If you feel up to it, have a look at the blinkwithoutdelay example in the reference.