The Schottky diode placed just after the incoming power connector J5 is there to protect the circuit from reverse polarity, ie applying the positive and negative the wrong way around.
If the incoming power to the anode of the diode is positive, the diode is forward biased and will allow current to flow. If this is reversed by mistake, and the incoming power to anode of the diode is negative, the diode is reverse biased and will block the flow of current, thus protecting the rest of your circuit.
A Schottky diode in particular has a lower forward voltage than other types of diode - typically a Schottky Vf is 0.4V, compared to 0.7V of a silicon diode.
The diode is chosen to allow enough current to flow (including peak to peak) with some safety margin. The 10A rating should be more than the total current consumption of the rest of the circuit.
The same is true of the voltage - if the power is plugged in backwards, the Schottky needs to be rated to block the reverse voltage.
Another factor to consider is the diode's power dissipation:
PD (Watts) = Forward Voltage across the diode * Forward Current flowing through the diode. This might be too high, depending on the application, and an alternative would be to use a P-channel MOSFET instead.
With the P-FET, the Power Dissipation can be calculated using (I^2)R from the RDS[on] resistance of the FET and the forward current, which is normally drastically less than that of a diode, Schottky or otherwise.
There are other disadvantages of course, such as cost and more components, but this is for the designer to consider.
I certainly find myself using P-FETs almost exclusivley for this purpose.