It is said that 8051 has an on-chip oscillator but requires external clock to run it. What may be the internal circuit for on-chip oscillator, how it runs after connecting crystal oscillator? Also what is the purpose of external capacitor with crystal oscillator?
I think you mean, "the 8051 has an on-chip oscillator but requires an external crystal"?
In other words, the amplifiers, etc, are on the chip, but you need to add an external crystal to make it run at the frequency you require.
This is not unusaal to any microcontroller.
Some can also run with a ceramic resonator instead of a crystal.
Many (most?) can also be driven from an external clock source.
As already noted, the Datasheet for the particular chip will give you specific details.
None of this has anything to do with Keil!