He means that the Count's memory didn't completely survive his death; he's still "developing", the way a child would be (emphasis mine):
"Well, in him the brain powers survived the physical death. Though it would seem that memory was not all complete. In some faculties of mind he has been, and is, only a child.
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This has certain consequences for our heroes, which gives them a slight advantage over him:
He isn't - at least not initially - as much of a big-picture thinker;
he tends to focus on the short-term goals (emphasis mine):
Well for us, it is as yet a child-brain. For had he dared, at the first, to attempt certain things he would long ago have been beyond our power.
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[D]oubtless, he had made preparation for escaping from us. But his child mind only saw so far.
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I have hope that our man brains that have been of man so long and that have not lost the grace of God, will come higher than his child-brain that lie in his tomb for centuries, that grow not yet to our stature, and that do only work selfish and therefore small.
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Rather than changing his behaviour in response to reason, he'll continue to repeat actions so long as he doesn't receive negative feedback (or until he grows in mind):
The little bird, the little fish, the little animal learn not by principle, but empirically. [...] [U]ntil he have the purpose to do more, he continue to do the same again every time, just as he have done before!
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Relatedly, he learns through trial-and-error experimentation rather than reasoning his way towards "optimal" results:
Do we not see how at the first all these so great boxes were moved by others. He knew not then but that must be so. But all the time that so great child-brain of his was growing, and he began to consider whether he might not himself move the box. So he began to help. And then, when he found that this be all right, he try to move them all alone. And so he progress, and he scatter these graves of him.
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However, Van Hellsing is quick to point out that Dracula is learning, and has been since the moment of his undeath, so this advantage is temporary at best:
But he is growing, and some things that were childish at the first are now of man's stature.
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