It’s all about adding positive reactivity.
In general, as others have said, rods are withdrawn, removing an impediment to neutron travel.
Reactors typically have a lot of energetic stuff going on in the first hours and even days after they are shut down (cf. my post here on decay heat), so there is a usually fairly substantial neutron population, so the reactor will start up fairly easily by just pulling the rods (slowly!).
If the plant has been shut down for many weeks, and if it is an older core, these factors may reduce the neutron population so low that the power level cannot be detected on instrumentation.
Then you need to follow an altered startup procedure: pull and wait. The reason for this is that “startup rate” is exponential, measured in “decades per minute”, or powers of 10 per minute. If you were to simply pull rods until the sleeping reactor came to life, the startup rate might very well be several decades per minute while the total wattage of the reactor was still less than a nightlight bulb—an unmeasurable power level. Then, by the time power was measurable on your instruments, it would be screaming up far faster than you could ever control it, and you would have an incident.
If pulling the rods does not add sufficient positive reactivity to wake the dormant reactor, then … I forget what happens—perhaps that’s end of life criteria. (I was a chem and rad tech guy, not a reactor operator—that’s the fellow with his hand on the control rod lever—and it has been 25 years).
Here’s a fairly detailed page written by a sub sailor describing the general reactor startup process, with some mention of the pull-and-wait startup.
And keep fighting that ignorance folks, the “moderator” in nuclear power terminology does not restrain the reaction; it is actually necessary to sustain the reaction (in a typical pressurized water reactor). Something else: a reactor that is critical is simply one that has a self sustaining reaction. Nothing bad about that.