CR stands for Combat Readiness, and it is an abstract measurment of a ship's fitness for battle. It represents crew effectiveness (affected by number, skill and fatigue) as well as the maintenance level of the equipment.
50% is neutral. Above that, ships get a small bonus to most statistics (damage, defenses, maneuverability, accuracy, etc.) scaling up to 10% at 100% CR. Below that, they get an equivalent penalty. Additionally, ships with particularly low CR (below 40%) can suffer malfunctions in combat, with varying severity depending on how exactly low CR is: from engines shutting down for a few seconds, through several weapons failing until the end of battle, to rapid unplanned disassembly of the hull.
Every ship has a maximum CR level, which depends on crew skill level and any bonuses from the commander's skills. Out of battle, it will slowly restore CR up to that level, consuming supplies to do so. Deploying a ship to battle costs some CR, usually around 15%, but it depends on the ship. A battle may cost less CR (up to half) if it was particularly short and one-sided, or it may cost more if the ship took hull damage or stayed in combat very long.
Every ship has a "peak performance" timer, which ticks down when in active combat (i.e. when close to a significant enemy force). When it reaches 0, the ship will begin losing CR. Smaller and higher-performance ships have longer timers, larger and lower-tech ships have longer timers.
CR has a bit different meaning for fighter wings. For them, it indicates the number of replecement fighters available. When a fighter is destroyed, a carrier will send out a new one to replace it. Every replacement costs CR, and when CR runs out, the fighter wing is done for the battle.
If you run out of supplies, you will begin losing CR, and when CR falls low, accidents will start happening. Those will increase with severity with lower CR, and will eventually ruin your fleet if you go without supplies too long.
I think that's it about CR. As for the tutorial: the reason it's not covered is simply that the last update to the tutorial was before CR was introduced into the game. I'm sure it will be covered eventually. The game is a work in progress.
There is a kind of tutorial for campaign mode, though, with pop-ups that explain some of the mechanics. I'm pretty sure it explains CR. Maybe you turned it off?