Nets function like any other weapon, except they are, like lances, one-use only. That is, they cause harassment, they can be repelled (length 5 weapon required as nets are length 4), and units with nets tend to waste them on already netted opponents. Shields apparently might not help to defend against nets (need to test/check).
Size 3 units have a 33% chance of not being affected by the net, size 4 units a 66% chance and size 5 and 6 are not affected. In addition, every point of strength above 15 add a 5% point chance of not being affected by the net.
Once under a net, a units gets a defense penalty [75% or 100%?], and cannot attack or repel or move. The strength check to get out is rolled against a 19.
Nets also carry weapon blesses on sacred units.
Source: discussion with the user Arco on discord, and some numbers given by Loggy. Some bit of testing for the nets being wasted on already netted units.