The levels indicate how much provocation is required before the sentinels will attack. Sentinels are provoked by killing animals, mining resources, or destroying reinforced objects or resource caches.
For example, on more permissive planets, you can kill an animal and get away with it, even if a sentinel sees. On stricter planets, they can get provoked by simply mining a large number of resources in front of them.
I believe it is also linked to how strong of a response you get once they begin attacking you. A stronger response can mean both a greater number of attacking sentinels and deadlier sentinels. There are powerful, ground-based sentinels that will show up when they get really mad.
On planets with the highest levels of activity (like Aggressive or Frenzied), your presence is provocation enough. Sentinels will attack on sight and immediately call in support.
It's worth noting that there is a correlation between sentinel activity and valuable resources. The sentinels' role is to protect nature, and what the player considers "rare", they consider "endangered".
After much time spent playing I have finally upgraded my exosuit to the max. 48 slots is the maximum you can have. 8 across and 6 down. The final upgrade costs 350,000 units. You will know that this is the last upgrade because no prompt to upgrade the exosuit is shown after the 48th slot.
Best Answer
There are four tiers of tech upgrades: Sigma, Tau, Theta and Omega. Their comparative strengths rank as follows:
Omega > Theta > Tau > Sigma
The stronger the upgrade, the rarer/more expensive the materials required to build it will be, as noted by @David Yell.
As noted by user @SGR, not every tech has four tiers -- four is the maximum you'll see, and the comparative ranks shown above still apply to techs with fewer tiers of upgrades.
(Source, Source, Source)