So there's a couple issues with your code, the first issue is that raw_input will always assume the input is a string and so your number1, operator, and number2 objects will be strings (and I assume you only want the operator variable to be a string). If you want to convert your numbers to floats, then you need to write something like number1 = float(raw_input ("What is the first number?"))
The second issue is that you need to start an if block with an if statement not an elif statement. elif statements come only after the if statement since it stands for "else if" - i.e. in the form if something else if something.
The third issue is that you didn't put quotes around your operators in your conditional statements. Python will not automatically assume they are strings. Python will assume they are variables which you haven't declared yet. You should have a statement like elif operator == '-' in order to make the comparison valid.
The fourth and last issue (that I see) is that since you are using raw_input it appears you are using python 2. Python 2 has a weird behavior when using the division operator / - namely it floors the division if the inputs to it are ints or longs. That behavior can cause a lot of headaches if you are not aware of it. You should probably include a from __future__ import division line at the beginning of your code so dividing doesn't floor the answer.