Fairly simple: say you have a bond worth $1,000 paying 4%, earning $40.
As an extreme, to help show the point, new bond rates drop to 3%.
Now a $1,000 bond only earns $30.
To earn the $40, the 4% bond is paying, you would need to invest $1,333.33 at the new 3% rate.
This makes your 4% bond worth very near $1,333.33.
I hope I made that clear, not sure.
Edit:
I reread and see I didn't answer the exact question, but with my example and,
bonds buyers thinking rates might go down, you can see why they might pay more
for a higher interest rate bond.