The BBB boot process is actually a series of steps that can be control based on inputs.  Changing the inputs can change how it boots.  Just because an SD card inserted does not mean all the boot processes are originating from the SD card. 
5 Stages to Booting:
Stage 1

• The ROM loads.   This is on board read only and can't change.  It looks for the MLO file and runs it.

Stage 2 (x-loader)

• MLO file runs and looks for Zimage

Stage 3 (u-boot)

• Zimage loads & run with configuration uEnv.txt
• uEnv.txt files have info on where to find the linux kernal plus lots of other parameters
• Parameters  can be passed from the uEnv.txt file into Linux kernal (provided the kernal was complied with the required modules for the parameters)

Stage 4

• Linux Kernal loads

Stage 5

• Root file system loads (e.g. debian, ubuntu, etc.)

Boot control:
The normal sequence is (S2 button not pushed):

• MC1 (eMMC on-board flash), MMC0 (SD card), UART0, USB0

S2 button pushed:

•  SPI0, MMC0 (SD card), USB0, UART0

Notes and Caution:

• Stage 2 and forward is basically software so it can be changed & modified.  Be careful what you read in blogs (this one!) and wiki as they could be out of date.
• Standard boot process can be overridden by placing a resistor between P8.43  and ground.  Pushing S2 is not required.
• S2 button push must have a power down/power up cycle.  Rebooting and pushing S2  has not impact.
• The BBB will boot from the SD card with out pushing S2.  However the stage 1 (MLO) and Stage 2 (U-boot) will be from the eMMC.
• Pushing S2 forces Stage 2 and Stage 3 to be pulled from SD card.
• Alternative remove MLO and Zimage from the eMMC to force boot from the SD card without pushing the S2 button
• Booting from eMMC will pull the uEnv.txt information from SD card if available.
• A blank SD card inserted will cause the BBB to hang.  The following is needed in a uEnv.txt file in the main partition of the SD card. 
• mmcdev=1 
• bootpart=1:2 
• mmcroot=/dev/mmcblk1p2 ro