A basis point exists because rates people need to talk about small moves without confusion. Saying yields rose 0.25% is ambiguous, since it could mean a quarter of a point or a quarter of the existing rate. Saying 25 basis points is not.
Everything in rates is quoted this way: a rate-hike is 25 or 50 bp, a credit-spread-bonds is 140 bp over Treasuries, a bid-offer in swaps might be half a basis point.
Example: the 10-year yield moves from 4.18% to 4.31%. That is a 13 basis point move. On $10,000,000 of a bond with a dv01 of $8,100, the position loses 13 x $8,100 = $105,300.
Related: dv01, rate-hike, yield-to-maturity