@Mufeed's answer is excellent, and well suited for beginners. This answer is a bit more complex.
One thing I would suggest is to write your letters using Python's multi-line strings. It makes them much easier to edit. My letters are a bit bigger and I've only defined the three letters b, g, and i (using artist mode in emacs..):
letter_definitions = {
    'b': Letter("""
      ****************
      ******************
      *****          *****
      ***              ***
      ***              ****
      ***              ****
      ***            ******
      ******************
      *********************
      ***             * *****
      ***               ******
      ***                 *****
      ***                  ****
      ***                  ****
      ***                  ****
      ***                ****
      ***          **********
      *********************
      *****************
        """),
    'g': Letter("""
               ****************
             *** *        **** **
            ***              *****
         ****
        ****
       *****
       ****
       ****
       ****            ************
       ****            *************
       *****                       *
       *****                       *
        *****                     **
         ******                   *
           *******               **
             *********       *****
                   *************
         """),
    'i': Letter("""
        +---+
        |***|
        +---+
         +-+
         |*|
         |*|
         |*|
         |*|
         |*|
         |*|
         +-+
    """),
}
The Letter class stores the shape, and records height/width/baseline (__init__ method), and can write itself to a 2-dimensional buffer (the add_to_buffer() method):
import textwrap
class Letter(object):
    def __init__(self, shape):
        # remove space to the left (textwrap.dedent)
        # and split the shape string into lines (self.shape is a list of strings)
        self.shape = textwrap.dedent(shape).split('\n')
        # remove any initial empty lines
        while self.shape[0] == '':
            self.shape = self.shape[1:]
        # remove any trailing empty lines
        while self.shape[-1] == '':
            self.shape = self.shape[:-1]
        self.height = len(self.shape)
        self.width = max(len(line) for line in self.shape)
        # we're doing the easy case where all letters are capitals
        # and the baseline is at the bottom
        self.baseline = self.height
    def add_to_buffer(self, buffer, x, y):
        "Write this letter shape to a 2-dimensional buffer at position x, y."
        # justify our baseline with the buffer's baseline
        y += buffer.baseline - self.baseline  
        # keeping track of which line and character we're at,
        # we go through each line in the shape
        for lineno, line in enumerate(self.shape):
            # .. and each character in the line
            for charpos, ch in enumerate(line):
                # and put the character into the buffer
                buffer[x + charpos, y + lineno] = ch
The buffer is implemented in the TextLine class, which creates a (simulated) 2 dimensional buffer of sufficient size to hold all the letter shapes by asking each letter how tall/wide it is:
class TextLine(object):
    def __init__(self, letters):
        self.letters = letters
        self.width = sum(letter.width for letter in self.letters)
        # one space between each letter, except the last one
        self.width += len(self.letters) - 1
        self.height = max(letter.height for letter in self.letters)
        self.baseline = self.height
        # add letters to buffer
        self.buffer = [' '] * (self.width * self.height)  # should probably use a buffer.buffer here..
        x = 0
        for letter in self.letters:
            letter.add_to_buffer(self, x, 0)
            x += letter.width + 1
    def __setitem__(self, (x, y), ch):
        # calculate the position and assign the character
        self.buffer[y * self.width + x] = ch
    def __str__(self):
        chunks = []
        # divide the buffer into pieces/chunks of length self.width..
        # (see https://stackoverflow.com/a/312464/75103 for how this works)
        for i in range(0, len(self.buffer), self.width):
            chunk = self.buffer[i:i + self.width]
            chunks.append(''.join(chunk))
        # .. and start each chunk on a new line
        return '\n'.join(chunks)
Finally I've renamed the print_big() function to big_text() and it returns the string to print:
def big_text(text):
    lines = text.splitlines(False)  # don't keep newlines
    res = []
    for line in lines:
        # convert each character to the corresponding Letter
        letters = [letter_definitions[ch] for ch in line]
        # put the letters into a TextLine
        text_line = TextLine(letters)
        # and append the buffer to the result
        res.append(str(text_line))
    return '\n\n'.join(res)
quite often you'll need to re-use functions like these, and it's easier to reuse them if they return the string rather than print it, and you can use it just as easy for printing:
print big_text('big')
The result:
****************                                             
******************                                           
*****          *****                    ****************     
***              ***                  *** *        **** **   
***              ****                ***              *****  
***              ****             ****                       
***            ******            ****                        
******************        +---+ *****                        
*********************     |***| ****                         
***             * *****   +---+ ****                         
***               ******        ****            ************ 
***                 *****  +-+  ****            *************
***                  ****  |*|  *****                       *
***                  ****  |*|  *****                       *
***                  ****  |*|   *****                     **
***                ****    |*|    ******                   * 
***          **********    |*|      *******               ** 
*********************      |*|        *********       *****  
*****************          +-+              *************