Meaning of "Remove Your Sandals"
Another passage where the shoe(sandal) is commanded to be removed is Joshua 5:15,
And it came to pass, when Joshua was by Jericho, that he lifted up his
eyes and looked, and, behold, there stood a man over against him with
his sword drawn in his hand: and Joshua went unto him, and said unto
him, Art thou for us, or for our adversaries?
14 And he said, Nay; but as captain of the host of the LORD am I now
come. And Joshua fell on his face to the earth, and did worship, and
said unto him, What saith my lord unto his servant?
15 And the captain of the LORD'S host said unto Joshua, Loose thy shoe
from off thy foot; for the place whereon thou standest is holy. And
Joshua did so.
In both instances; Moses and Joshua, the shoe, being "profane", is removed at the request of the Angel of the Lord. In the case of Moses, it is God Himself, in the case of Joshua, it is the Captain of the Army of the Host of God; what is important is that the place of the Lord's "Presense" is holy, and therefore the shoe is to be removed before the holiness of God.
Our first source of information concerning the shoe is the Bible. Here
the shoe partakes of the character of the profane, symbolizing the
Earthly in contrast with the Holy. Removing the shoes signifies
putting off something profane, obligatory upon those who approach the
Holy."Put off thy shoes from off thy feet, for the place whereon thou
standest is holy ground", is the command to Moses.(Taken from Jacob Nacht-Symbolism of the Shoes in Reference to Jewish Sources/JQR)
Another point which Jacob Nacht mentions is:
"The Levites, whose function it was to carry the vessels of the
Tabernacle, were required to take off their shoes while performing
this holy service. The priests, likewise had to be barefooted when
performing their service in the Sanctuary; this regulation has in part
continued to be observed to this very day on occasion of the Priestly
Blessing pronounced on festivals."(ibid)
The understanding is from Ex. 30:18-21,
Thou shalt also make a laver of brass, and his foot also of brass, to
wash withal: and thou shalt put it between the tabernacle of the
congregation and the altar, and thou shalt put water therein.
19 For Aaron and his sons shall wash their hands and their feet
20 When they go into the tabernacle of the congregation, they shall
wash with water, that they die not; or when they come near to the
altar to minister, to burn offering made by fire unto the LORD:
21 So they shall wash their hands and their feet, that they die not:
and it shall be a statute for ever to them, even to him and to his
seed throughout their generations.
The understanding is that the Temple contained the Presense of God, in 2 Chr. 5:14 we read,
So that the priests could not stand to minister by reason of the
cloud: for the glory of the LORD had filled the house of God.
Therefore, the whole "Sanctuary" was holy ground, and the priests and Levites who ministered there, from the clothes they wore to the bare soles of their feet, were mindful of this, that they were in the Presense of God and had to be 'circumspective', lest they die.
Angelic Visitations in General
The 2 passages where the Angel of the Lord commands to remove one's sandals implies that the subject recognizes the Holiness of a Holy God, and it is communicated as such. In the instances of Gen. 16:7-14, Gen. 22:11-15, Num. 22:22-38, Judges 6:11-23, and 13:3-22, the angel appears as a messenger to send relief, comfort, or carry a particular message. Also, in the cases of Hagar and Balaam, it's questionable whether or not they would recognize the requirement of holiness in the Presense of God; the burden is "too great" for unregenerate men to come into the Presense of God. A key example of this is in 1 Sam. 5:9, after the Philistines had captured the Ark of the Covenant, the most sacred object in the Temple, located in the Holy of Holies,
And it was so, that, after they had carried it about, the hand of the
LORD was against the city with a very great destruction: and he smote
the men of the city, both small and great, and they had emerods in
their secret parts.
'Emerods', or "hemorrhoids" as they are commonly called, are usually a result of "straining" in bowel movements, and other activities. Verse 11 says,"the hand of God was very heavy there," which for those who have no concept of the holiness of God, can be very heavy indeed. The result was they put the Ark on a cart, drawn by 2 cows with a trespass offering; representative of the 'trespass' which they made on the Ark of the Covenant(the Holiness of God manifested to the children of Israel).
"To remove one's sandals from one's feet" is to acknowledge the Presense of God, and the consecration that Presense demands. Angelic visitations may or may not require such consecration, but those who ministered in the Lord's courts were required to carry such consecration-the sign of which was to 'bare one's feet'.