These terms refer to multiplayer matches and how after a lot of experience the flow of how conflicts in sins tend to evolve.
Early game- Rush or get a strong economy..or try to do both in some form of "middle style" of play.
Easily acquired labs 1-2, possibly 3, early investment in these don't really hamper your match. Going beyond 3 labs is inviting a substantially weaker defense against an opponents rush, so be careful when doing this. Scout Scout Scout!
If you are in the "suicide spot" (a guarenteed early game 2v1 with no allies nearby to call for aid), your only hope is to get a colonizer capital and have it avoid the enemy and colonize somewhere far away. You will need a fleet to hamper opponents economy buildup. Your job is to buy as much time as you can.
Priorities of the early game-
Hammering your opponent into submission, and or gaining strategic choke point planets to ensure a strong long term strategy. For economy players you are trying to ensure the most efficient gain of "resource rate"(how many resources you get per second).
Early mid game- this is preperation for the mid game, what ships you will have, whether or not you have the ability to economy up.
If your rush succeeds, you wipe/persue your opponent off the map, and start to build an economy(if you can).
You may need to send your fleet in to help an ally with a 2v1 scenario.
If your rush stalemates, you will attempt to beg your economy player for early feed, or try to gain every economic advantage while still watching your opponents fleet buildup.
If you built to rush to a titan, this is about when your titan would be finished.
If your opponent has lasted this long, their economy player now has enough credits to provide a substantial feed, and if you notice them getting a lot of resources then you should call for feed yourself.
Mid game- This is about striking at the opponents economy players and/or defending against them.
This is when your economy players should starbase the homeworlds of hotley contested fights to free up home defense. Also, this is when the economy player needs to carefully decide when to build a fleet, and when not to.
Mid late game- This is when your fleets are getting near max strength and huge battles between thousands of ships start to occur. You have at this point researched the majority of the critical technologies that you really need.
End game- this is where you face maxxed endgame fleets, and start to finish all the research. This is really rarely achieved in multiplayer, but when it is it can be a really fun match. Reaching this point requires a relatively economically balanced map, with all players playing well with relatively equal skill matchups.