Because x=1 is a statement, not an expression. Use exec to run statements.
>>> exec('x=1')
>>> x
1
By the way, there are many ways to avoid using exec/eval if all you need is a dynamic name to assign, e.g. you could use a dictionary, the setattr function, or the locals() dictionary:
>>> locals()['y'] = 1
>>> y
1
Update: Although the code above works in the REPL, it won't work inside a function. See Modifying locals in Python for some alternatives if exec is out of question.
x = 0
def assignNewValueToX(v):
global x
x = v
eval('assignNewValueToX(1)')
print(x)
It works... cause python will actually run assignNewValueToX to be able to evaluate the expression. It can be developed further, but I am sure there is a better option for almost any needs one may have.