Logistics points are required for building units and claiming resources. Also outposts cost logistics points.
I think what happened is one of your cities leveled up and thus you got more logistics points. I havent seen this documented anywhere in the game but I think cities get +1 logistics for every 2 levels. You see logistics near mana and other resource counters in the UI.
Other ways to get logistics points:
*Building - barracks, command post,town hall, etc
* Logicians - you can get these from quests, the sorcerer king offers(I always choose this option),and as offerings from certain minor factions. they are the blue administrators. I dont think you need to station them in a city. I would put them there because its safer but you still get the logistics bonuses when he is outside a city.
*Spells - one of them gives +1 logistics(takes a city essence slot), eternal supply(require 4 enchantment spell books) give +1 logistics per essence
*units you get from quests dont use logistics - those are "free"
I wouldnt try to build as many cities as fast as possible - focus on shards first. I've won games with only 1 - 2 cities. The main reason you would want more cities are more logistics buildings and more libraries/ other recipe granting building. Also you can use cities to produce mana. But shards are much,much more important. If you do build a lot of cities you can sort of defend them all with one army using the cloud walk spell. Thats what I usually do. You can also use upgraded outposts - they cant be destroyed and damage enemy units in their territory.
As far as battles and units are concerned, which sovereign are you playing? Some of the early units are really weak and almost not worth building.If you are playing the wizard you're almost forced to use ice blast and flame dart to tilt early battles in your favor.
Try to craft as much gear as possible in the early game - the leather boots and curass will help with your units surviveability. You can equip your units with gear you craft. I usually try to work my way towards sentinels armed with hunters short swords.
Let me know if you have any other questions or if I missed something.