Incarnate means "existing with a bodily form, especially of a human body," so the term "incarnate spirit" (not to be confused with the pagan idea of "reincarnation") seems like a paradox, and yet throughout The Bible, spirit beings appeared from time to time with a physical body. The greatest example of that is Jesus Christ as He appeared to many people in the time between His resurrection and ascension. Angels also often appeared as humans (e.g. Genesis 19:1,5), although it's interesting to note that, at least as far as it's recorded in the Bible record, righteous angels always appeared as themselves, in human bodily form, while demons usually "appeared" only by "possessing" existing humans (e.g. Mark 5:2-13, see also Casting Out Demons).
In the time between His resurrection and ascension, the Messiah appeared, differently, to numerous people. He sometimes appeared with the body that had suffered the grievous wounds of the crucifixion, and as such was recognized by those who knew Him, but He also appeared differently so that those who knew Him did not recognize Him (although they did eventually also realize that the man that they didn't recognize was Jesus Christ). He appeared physically, as He plainly said, and yet He was able to appear and disappear at will.
"And as they thus spake, Jesus Himself stood in the midst of them, and saith unto them, Peace be unto you. But they were terrified and affrighted, and supposed that they had seen a spirit. And He said unto them, Why are ye troubled? and why do thoughts arise in your hearts? Behold My hands and My feet, that it is I Myself: handle Me, and see; for a spirit hath not flesh and bones, as ye see Me have. And when He had thus spoken, He showed them His hands and His feet. And while they yet believed not for joy, and wondered, He said unto them, Have ye here any meat? And they gave Him a piece of a broiled fish, and of an honeycomb. And He took it, and did eat before them." (Luke 24:36-43 KJV)
"When He was at table with them, He took the bread and blessed, and broke it, and gave it to them. And their eyes were opened and they recognized Him; and He vanished out of their sight." (Luke 24:30-31 RSV)
"After this He appeared in another form to two of them, as they were walking into the country." (Mark 16:12 RSV)
"Just as day was breaking, Jesus stood on the beach; yet the disciples did not know that it was Jesus ... Jesus said to them, "Come and have breakfast." Now none of the disciples dared ask Him, "Who are you?" They knew it was the Lord. Jesus came and took the bread and gave it to them, and so with the fish. This was now the third time that Jesus was revealed to the disciples after He was raised from the dead." (John 21:4,12-14 RSV)
Fact Finder: Have some people talked with angels without realizing that they were angels?