Consider five coin tosses. I would call each of the possible outcomes a microstate (for example, HTTHT, THHHT, HHHTH, TTTTT and so on. H stands for heads and T for tails).
Now suppose I define a variable such as X=Total number of heads. For the microstates I have mentioned above, X will take values 2, 3, 4, 0 and so on. X is a macrostate. It tells you nothing about the specific configuration of the system. For example, X=4 will correspond to five microstates (HHHHT, HHHTH, HHTHH, HTHHH, THHHH), but you have no way of knowing which one.
An accessible state is a microstate the system can take without violating any laws governing the system.