God made Aaron’s rod bud — it was a miracle. In Numbers 17:5 God says:
…the staff of the man whom I choose shall sprout. Thus I will make to cease from me the grumblings of the people of Israel, which they grumble against you.
After the rebellion in Numbers 16 (see especially Num. 16:3), God made Aaron’s staff bud to show that he had chosen Aaron to be the High Priest.
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Further investigation:
There is possibly an interesting connection to this event in Hebrews 4:14-5:10, which talks about Jesus as our high priest.