The naive, non-atomic implementation:

1. reads the value in the memory location;
2. adds one to the value;
3. writes the new value back into the memory location.

Now, imagine two processes are running incrementing a single, shared memory location:

1. the first process reads the value in memory location;
2. the first process adds one to the value;

but before it can write the new value back to the memory location it is suspended, and the second process is allowed to run:

1. the second process reads the value in memory location, the same value that the first process read;
2. the second process adds one to the value;
3. the second process writes the new value into the memory location.

The second process is suspended and the first process allowed to run again:

1. the first process writes a now-wrong value into the memory location, unaware that the other process has already updated the value in the memory location.