Well, “memory” is basically a huge array of bytes. However, most larger things like integers need more than 1 byte to store them — a 32 bit value, for example, would use 4 consecutive bytes of memory.
Now, the memory modules in your computer aren’t usually “bytes”; they are also organized with a few bytes “in parallel”, like blocks of 4 bytes.
For a CPU, it’s much easier = more efficient = better performance to not “cross” such block-borders when reading something like an integer:
memory byte 0 1 2 3 4 5 6 7 8 9 10 11
integer goooood
baaaaaaaaad
This is what the “alignment” says: an alignment of 4 means that data of this type should (or must, depends on the CPU) be stored starting at an address that is a multiple of 4.
You observation that sizeof==alignof is incorrect; try structures. Structures will also be aligned (because their individual members need to end up on the correct addresses), but their size will be much larger.