Although true, that's not what the question asked:

"What is meant by vectored interupt?"

He wants the meaning of the term - not a description of what the 8051 specifically does.

"Does it mean that when an interupt occurs a certain program address is used. At that address is the address of the subroutine?"

Yes, that would be my understanding of a "Vectored" interrupt.

This is what, for example, the x86 family does (in Real Mode, at least).

Note, however, that this is not what the 8051 does!
The 8051 has one less level of indirection; ie, when an interrupt occurs, the program jumps to a certain program address and executes the instructions starting at that address
Of course, the code it finds there may be a jump to your own subroutine somewhere else...

"Can the first address be changed."

Not in the 8051 nor the x86.
However, IIRC, the x86's vector numbers for user-defined interrupts can (must?) be set by the interrupt controller (or by the system for software interrupts).

"I assume the second one can be."

Thst is the whole point of a Vector Table!