What is a minecraft singleplayer/integrated server?

Question

Recently set my Minecraft launcher to stay open when I play, and noticed the logs that displayed in the background mentioned "singleplayer server", and I was confused as I thought that servers were network based. So I looked up the definition and I got:

a computer or computer program which manages access to a centralized resource or service in a network.

I don't understand the first part, but I get the gist of the second. Can someone please explain to me what this means, because I have searched online but I can't find anything on this topic. If it is a singleplayer server, also, is there access to a vanilla console?

Here is a log for when I started and paused my singleplayer world:

[17:18:37] [Server thread/INFO]: Starting integrated minecraft server version 1.11.2
[17:18:37] [Server thread/INFO]: Generating keypair
[17:18:38] [Server thread/INFO]: Preparing start region for level 0
[17:18:39] [Server thread/INFO]: Preparing spawn area: 36%
[17:18:39] [Server thread/INFO]: Changing view distance to 12, from 10
[17:18:40] [Server thread/INFO]: CaolanMC[local:E:ac0c53d9] logged in with entity id 44 at (996.5877881075121, 4.0, -763.9979757512565)
[17:18:40] [Server thread/INFO]: CaolanMC joined the game
[17:18:41] [Server thread/INFO]: Saving and pausing game...
[17:18:41] [Server thread/INFO]: Saving chunks for level 'Selective  Weapons'/Overworld
[17:18:41] [Server thread/INFO]: Saving chunks for level 'Selective  Weapons'/Nether
[17:18:41] [Server thread/INFO]: Saving chunks for level 'Selective  Weapons'/The End

Answer 1

tl;dr - As the name suggests, it is a server, only that it's part of the game itself.

An integrated server is as the name suggests, a server that is integrated into the game itself.

Prior to Minecraft 1.3, the game ran on one main thread. It either:

• Simulated the Minecraft world, as it should (Single Player), or:
• Just render the Minecraft world, sending inputs and receiving outputs to/from a server. (Multiplayer)

In Minecraft 1.3 however, with the introduction of commands, the "Open to LAN" button, and the integrated server. Multiplayer behaved like it should, but Single Player however, starts a server that runs on a separate thread that could only be connected to by others on the same network (if opened to LAN) or by nobody else.

While this may seem nothing at all, it is essentially a reshuffle of Minecraft's codebase. Rather than tie in Minecraft's game logic (ie. mob pathfinding and world simulation) with the game's engine, it separated the graphics engine from the game logic.

In turn, from a programming standpoint, this makes it easier to add new features, while at the same time, not make each frame draw slower due to some complicated logic running in the background (ie. lots of water spreading).

See Wikipedia for a more generalized in-depth explanation

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Is this unique or used by multiple games?

By 'games', I'm assuming you mean 'software'.
No, it is not unique to Minecraft.

An example of a game using it is Dungeon Defenders. Games are run on a server that is built into the game, regardless it is through Trendy.NET or offline through LAN. The same applies for whether it's open for other players, or on your own.