We don’t know exactly what kind of speech impediment Moses had but Scripture indicates that he did have an issue of some kind:
Moses, however, said to the LORD, “If you please, my Lord, I have never been eloquent, neither in the past nor now that you have spoken to your servant; but I am slow of speech and tongue.”
-Exodus 4:10
However, Moses protested to the LORD, “If the Israelites did not listen to me, how is it possible that Pharaoh will listen to me, poor speaker that I am!
-Exodus 6:12
Common tradition has assumed that Moses had a stutter since Exodus 4:10 indicates that his “slow speech and tongue” had been with him for a long time (“neither in the past”). Usually people who purposely slow down their speech are people who have issues with stuttering. However, its also possible that Moses just wasn’t a good public speaker or quick on his feet when it came to speaking. Maybe he just had a tendency to freeze up when speaking in public (i.e. stage fright).
In Jewish midrash Moses injured himself as a small child when he put a burning coal in his mouth.
Either way, Moses had some kind of issue that prevented him from being confident when speaking and God’s grace helped him to overcome it.
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