Electronic – the significance of 111 in clock speed

Your question suggests that the SPI is the input from the ADC. However, the ADS825E is a parallel output device. So, is the SPI the output from the microcontroller? I'll presume it is.

You'll always need a faster clock. Even for a RISC controller running 1MIPS/MHz a 40MHz clock will allow you to execute 40M read instructions per second, but you have extra code, at least a jump instruction to create a loop. So at 80MHz you can read, and jump to the read instruction. But that's not all. If you want to shift the read data out through SPI that will need to be clocked as well. At least 10 clock pulses per read sample, to be precise. Unless you're using an asynchronous microcontroller (I don't know if they already exist outside of the lab yet) that means 400MHz. At least.
You can do this with some high end ARM controllers, but if you just want to read and shift out there are better solutions. Oli mentions an FPGA, but a CPLD will probably do.

A microcontroller isn't aware of a thing like time; it only knows clock ticks. So the controller's logic can't tell the difference between running at 16 MHz and 192 MHz: a clock tick is a clock tick, and it will do exactly the same in 10 clock ticks for both frequencies.

That means that when actual time is relevant it's up to you to make sure the number of clock ticks gets properly translated to time. Suppose you have a 1 ms timer for the 16 MHz controller. It will give you an interrupt every 16 000 clock ticks, that's once every ms. Run that same code on a 192 MHz controller and you'll still get the interrupt every 16 000 clock ticks, but now that will be 83 µs. So change the timer's value to 192 000. Do this for everything to which real time is relevant. If you don't the 9600 bps UART will run 12 times too fast, so set the prescaler to a 12 times higher value.

The ADC is a bit different. That one does know about time: the measurement capacitor will droop at the same rate whether you run at 16 MHz or at 192 MHz. Or at 1 Hz. While the controller will run (or rather: "stroll") happily at 1 Hz, for the ADC that's too slow. The datasheet will tell you the minimum frequency it needs.