C - Using bit-shift operators for base conversion

I'm trying to convert some data from hex to base64 in C, I found an algorithm online but I would really like to know how it works rather than just implenting it and firing it off. If someone could please explain how the following is working I would appreciate it. I have been reading about the shift operators and I don't seem to understand them as much as I thought I did...it's not quite clicking for me.

for (x = 0; x < dataLength; x += 3) 
{
  /* these three 8-bit (ASCII) characters become one 24-bit number */
  n = data[x] << 16;

  if((x+1) < dataLength)
     n += data[x+1] << 8;

  if((x+2) < dataLength)
     n += data[x+2];

  /* this 24-bit number gets separated into four 6-bit numbers */
  n0 = (uint8_t)(n >> 18) & 63;
  n1 = (uint8_t)(n >> 12) & 63;
  n2 = (uint8_t)(n >> 6) & 63;
  n3 = (uint8_t)n & 63;

This code was taken from Wikibooks, it is NOT mine, I'm just trying to understand the bitshifting and how it's allowing me to convert the data.

Thank you for your help, I really appreciate it.

Source: Base64