When it comes to pudding the "soft set" means that the pudding sets to a texture that is thick enough to hold its shape but still relatively soft and creamy, like a custard.
Soft set pudding is not as firm as a set jelly, but it does have some structure and will hold a pile when spooned.
Instant pudding mixes often require a soft set after it's been mixed with milk, which means the soft set pudding will thicken to a soft and creamy consistency within a couple of minutes, often within the time that is specified on the soft set pudding packages.