First thing, its Combat Readiness, not "Crew" Readiness. Just pointing it out to ease the concept. Let me try and explain it.
Combat readiness is the capability of a ship to engage in combat. It's been akined to having the cargo locked down, the crew to battlestations, weapons loaded, damage controlled and repairs issue.. that sort of stuff. You also have to understand the background lore points to the technology behind the ships workings and such being almost forgotten, and in general, a harsh and unforgiving place.
That combat readiness is dictated by a lot of factors from crew, the presence of an officer (you/flagship), damage taken, any refits done recently (outside a station) and other such items. I assume you're interested in maximum combat readiness and how to increase it since i have the opinion that you're going way over some limits.
Your capability as a commander allows you to oversee the logistical capabilities of your fleet, the act of maintaining an efficient and proper organized fighting force. That is represented in the logistics bar. From ships to crew and marines, each of the resources need a careful guiding hand and attention. Thus, they drain on your supply/day and increase the logistics bar, which is exactly around how much supplies you can juggle per day. Ideally you'd sit inside the limit, but carrying extra cargo, more people, more strain than you can manage will lead to very serious max CR limits (even saw -60%) which can force your fleet under its deploying need and you end up with 'dead' ships. If i know correctly if you use less, you might get a bonus to max CR, but don't quote me on that.
Second thing is crew and officers. So far we only have one officer, you, which increases the max CR of a ship by 10%. As for crew, each crew level adds 10% more max CR. With a full elite crew ship and you 'flagshipping it' you can get 100% CR.
As for recovering, be careful that at stations you need one to repair, and again to regain CR. Also, it can be grayed out even if it's unneeded, or if you don't have enough supplies to regain CR. Check up with the hover over text to see how much you need.
If the above is followed and you have max CR positive, supplies and time, if not repairing at a station, you should regain CR per day as listed in your fleet panel.