How to make program go back to the top of the code instead of closing

Use an infinite loop:

while True:
    print('Hello world!')

This certainly can apply to your start() function as well; you can exit the loop with either break, or use return to exit the function altogether, which also terminates the loop:

def start():
    print ("Welcome to the converter toolkit made by Alan.")

    while True:
        op = input ("Please input what operation you wish to perform. 1 for Fahrenheit to Celsius, 2 for meters to centimetres and 3 for megabytes to gigabytes")

        if op == "1":
            f1 = input ("Please enter your fahrenheit temperature: ")
            f1 = int(f1)

            a1 = (f1 - 32) / 1.8
            a1 = str(a1)

            print (a1+" celsius") 

        elif op == "2":
            m1 = input ("Please input your the amount of meters you wish to convert: ")
            m1 = int(m1)
            m2 = (m1 * 100)

            m2 = str(m2)
            print (m2+" m")

        if op == "3":
            mb1 = input ("Please input the amount of megabytes you want to convert")
            mb1 = int(mb1)
            mb2 = (mb1 / 1024)
            mb3 = (mb2 / 1024)

            mb3 = str(mb3)

            print (mb3+" GB")

        else:
            print ("Sorry, that was an invalid command!")

If you were to add an option to quit as well, that could be:

if op.lower() in {'q', 'quit', 'e', 'exit'}:
    print("Goodbye!")
    return

for example.

Python, like most modern programming languages, does not support "goto". Instead, you must use control functions. There are essentially two ways to do this.

1. Loops

An example of how you could do exactly what your SmallBasic example does is as follows:

while True :
    print "Poo"

It's that simple.

2. Recursion

def the_func() :
   print "Poo"
   the_func()

the_func()

Note on Recursion: Only do this if you have a specific number of times you want to go back to the beginning (in which case add a case when the recursion should stop). It is a bad idea to do an infinite recursion like I define above, because you will eventually run out of memory!

Edited to Answer Question More Specifically

#Alan's Toolkit for conversions

invalid_input = True
def start() :
    print ("Welcome to the converter toolkit made by Alan.")
    op = input ("Please input what operation you wish to perform. 1 for Fahrenheit to Celsius, 2 for meters to centimetres and 3 for megabytes to gigabytes")
    if op == "1":
        #stuff
        invalid_input = False # Set to False because input was valid


    elif op == "2":
        #stuff
        invalid_input = False # Set to False because input was valid
    elif op == "3": # you still have this as "if"; I would recommend keeping it as elif
        #stuff
        invalid_input = False # Set to False because input was valid
    else:
        print ("Sorry, that was an invalid command!")

while invalid_input: # this will loop until invalid_input is set to be False
    start()

Python has control flow statements instead of goto statements. One implementation of control flow is Python's while loop. You can give it a boolean condition (boolean values are either True or False in Python), and the loop will execute repeatedly until that condition becomes false. If you want to loop forever, all you have to do is start an infinite loop.

Be careful if you decide to run the following example code. Press Control+C in your shell while it is running if you ever want to kill the process. Note that the process must be in the foreground for this to work.

while True:
    # do stuff here
    pass

The line # do stuff here is just a comment. It doesn't execute anything. pass is just a placeholder in python that basically says "Hi, I'm a line of code, but skip me because I don't do anything."

Now let's say you want to repeatedly ask the user for input forever and ever, and only exit the program if the user inputs the character 'q' for quit.

You could do something like this:

while True:
    cmd = raw_input('Do you want to quit? Enter \'q\'!')
    if cmd == 'q':
        break

cmd will just store whatever the user inputs (the user will be prompted to type something and hit enter). If cmd stores just the letter 'q', the code will forcefully break out of its enclosing loop. The break statement lets you escape any kind of loop. Even an infinite one! It is extremely useful to learn if you ever want to program user applications which often run on infinite loops. If the user does not type exactly the letter 'q', the user will just be prompted repeatedly and infinitely until the process is forcefully killed or the user decides that he's had enough of this annoying program and just wants to quit.

You can easily do it with loops, there are two types of loops

For Loops:

for i in range(0,5):
    print 'Hello World'

While Loops:

count = 1
while count <= 5:
    print 'Hello World'
    count += 1

Each of these loops print "Hello World" five times