A random forest of 500 trees is built from the same data. Each tree is trained on a bootstrap sample and, at every split, considers only a random subset of the features.
Why does the random feature subset at each split improve the forest?
Why did you pick that answer? Two or three sentences. The act of articulating it is what builds the judgment — not the click that follows.
Averaging reduces variance only to the extent the things being averaged disagree. If every tree could use the strongest feature at the root, the 500 trees would look alike and their errors would be shared. Forcing each split to choose among a random subset makes the trees different — individually a little worse, collectively much better. Bagging supplies the diversity in rows; feature sampling supplies it in columns.
Individual trees typically get slightly worse — they are sometimes denied their best split. The gain is in the ensemble, not the member.
It is faster, but the statistical purpose is decorrelation. Breiman introduced it to improve accuracy, not runtime.
A strong feature is a good feature. The forest still uses it — just not in every tree at every split.