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If leukemia (and many cancers) aren't contained in their growth, then the cell count increases. Now slowing is a good thing, but there are different constraints as to why it stops. If the count levels off, then that is a great sign that the "acute" phase is over and it is now chronic. You can live with chronic leukemia for decades and decades. It runs in my spouse's family. There is literally not a person in her family over the age of 45 without some form of diagnosed leukemia. Some have literally lived into their 90s without problem (one would have made 100, if it wasn't for a completely different injury). Now, everyone is different but cancers aren't the death sentence they used to be. The fact that you are in watchful-waiting, rather than having active intervention is a good sign, a very good sign.

A smear is where the hematopathologist looks at a sample of your blood. They basically figure out what is wrong with your organ systems based on the damage they see in the cells. They can also give powerful information on treatment options and are a key part of the care team. (Not to be biased, since I know a few, but pathologists in general are unsung heroes in the medical field since they aren't on the "front lines.)
A differential is where they count the relative proportion of blood cells, which can be used to get their exact count. This lets you know if you are immuno-compromised (which is unlikely given the WBC you gave and the WW by the doctor) and all sort of other data in the hands of a skilled oncologist and care team.

But if you just remember three things from this post, let them be:

1. Being vigilant is not the same as letting it control your life.
2. You are more than your condition: it does not define you, like that scar you got as a kid doesn't either.
3. A diagnosis is not a death sentence, but a reminder of the life you have.