The example is describing what happens when you try to read a block of 4 consecutive bytes on a CPU with double-byte access granuality. On this type of CPU, memory is accessed as pairs of bytes, always starting with an even-numbered byte.
If you try to read the block starting with byte 0, it has to perform 2 reads: bytes 0-1 and bytes 2-3.
If you try to read the block starting with byte 1, it has to perform 3 reads: bytes 0-1 (to get byte 1), bytes 2-3, and bytes 4-5 (to get byte 4).
Memory access granularity is the number of bytes it accesses at a time, and a memory access boundary is where each of these groups of bytes begins. The groups of bytes are always addressed at even multiples of the granularity -- if it's double-byte granularity they start on even addresses, if it's quad-byte granularity they're at multiples of 4.
As an analogy, consider an apartment building with 4 units on each floor. Units 0-3 are on floor 0, units 4-7 are on floor 1, etc. If you want to slip a flyer under the doors of units 0-3, you only have to go to one floor. But if you want to slip a flyer under 1-4, you have to go to 2 floors: floor 0 for 1-3, floor 2 for unit 4.