A chabad.org article titled "Why the Spoon and the Feather?" addresses this. The reason given for the candle is a practical one: so that we can see the bread.
In terms of the spoon and feather:
We search with a wooden spoon so that we can burn it later. We read in the Code of Jewish Law
[SA Orach Chaim 445:3, see Rama] that if one does not find any leavened foods during his search, he should burn the vessel with which he searched.
This can be easily accomplished with a wooden spoon. Even nowadays, when we put out ten pieces of bread (so we always find something leavened), there is still significance to burning the bread specifically in a wood-fueled fire.
The feather serves a practical purpose. We can use it to sweep up any crumbly bits of leavened food that we may encounter.
Wikipedia gives another reason for the feather:
"[a feather is] used throughout the year to 'egg' the challah, and is therefore burnt in the chametz."