Average forward current:
Electric current generates heat. If current through the diode is too large, the heat will destroy P-N junction.
In general when designing a power supply, it is inteligent to use diodes with an Io rating of at least 1.5 times expected average direct current forward current. If this current is 4.0 A, rectifier diodes should be rated at Io = 6.0 A or more. Certainly, it would be wasteful of money to use the 100-A diode in a circuit where average forward current is 4.0 A.
The Io flows through the diodes. The current drawn by load is quite different from this. Also, Io is an average figure. The instantaneous forward current is the other thing, and can be 15 or even 20 times Io, depending on nature of power supply filtering circuitry.
Some of the diodes have heatsinks to help carry heat away from P-N junction. A selenium diode can be recognized by appearance of its heatsink as given in the figure below.
Figure-- A selenium rectifier can be recognized by its heatsink.
Diodes are connected in parallel to increase current rating. When this is done, small value resistors are placed in series with each of the diode in the set to equalize the current burden among diodes. Each resistor should have a voltage drop of around 1 V.
Figure-- When diodes are connected in parallel, resistors help equalize current load.