Five score years ago, a great American, in whose symbolic shadow we stand today, signed the Emancipation Proclamation.
"In whose symbolic shadow we stand today" is a subordinate clause and specifically a relative clause.
We could instead say "whose symbolic shadow we stand in today" - this preserves the normal word order of the phrase "stand in", as in "standing in (someone's) shadow".
But in formal usage you quite often see the preposition moved forwards so that it precedes the relative pronoun ("whose", "whom", "which").
So "the glass that I drank from" can also be phrased as "the glass from which I drank", and "the person that I gave the book to" can be worded as "the person to whom I gave the book". This sounds stilted (overly formal) in everyday speech. In everyday speech it's much more normal to have the preposition at the end.
If you are asking why a relative clause is used at all:
You could say "we stand in his symbolic shadow today" (without "whose") but this would then be a separate sentence, although it could be parenthetical (within brackets or dashes): "Five score years ago, a great American (we stand in his symbolic shadow today) signed the Emancipation Proclamation."
The use of a relative clause makes the sentence flow better than a parenthetical remark would, though, and the elevated or literary tone of "five score years" fits with the literary style of the rest of the sentence (including "in whose").