The system is both overly complicated and very poorly explained. First, there are actually two different systems, Status and Affinity. Both systems use the terms CHICK/DIK, but they work differently.
Status is determined by a host of small actions the MC can take, like checking out various girls or cheating at tests (+DIK points), or not checking out girls and passing tests fairly (-DIK points, leading to CHICK status). Status is broken into 3 levels (from least to most extreme: normal, Huge, and Massive), plus Neutral in between. The more positive or negative points you have, the more extreme your Status. Status is mostly about how the MC speaks: dialog with CHICK Status tends to be polite and measured, while DIKs are more crude and profane. Early on in the game, Status was also used to gate certain actions (you need Huge DIK status to check Sage's g-string in Episode 1, for example). By Season 2, however, that has almost vanished and Affinity gates actions instead.
Affinity is the net result of all the "Major Decisions" the MC takes. Each decision removes one box on the opposite side of the status bar: for example, choosing to accept Quinn's restaurant offer in Episode 1 is a DIK major decision, so it removes the outermost box on the CHICK track. Likewise turning down Quinn's offer removes the outermost DIK box. As we proceed through the game, the status bar is thus whittled down over time. Affinity is the net result of those choices. If you have made 2+ more DIK major decisions than you have CHICK major decisions, you gain DIK Affinity, and vice versa. If you have made 0-1 more of one type of decision than the other, you have Neutral Affinity. Unlike Status, there are no further gradations for Affinity.
Starting late in Season 1, Affinity began to take over the role of gating the MC's actions. Showering with Jill in Episode 4 required CHICK Affinity, for example, whereas Quinn will only allow the MC to help her in Episode 6 if he has DIK Affinity (in addition to some other requirements). As a side effect of losing boxes, Affinity can indirectly limit Status: lose enough boxes on the CHICK side, for example, and you can no longer get enough points to become a Massive CHICK. Since Status checks are few and far between these days, this doesn't make much difference unless you run completely out of boxes on one side.
If that happens (which first became possible late in Episode 6), the MC would gain permanent Affinity. This means the MC is no longer capable of making contrary major decisions (though it looks like in Season 3 he will now have a neutral option that's sort of a non-committal answer to the dilemma). If the MC manages to make it to through the final Major Decision in Episode 8 without losing all his CHICK and DIK boxes, he'll gain permanent Neutral Affinity instead.
So that's the system in a nutshell. It's not that Affinity determines which LI routes you can follow directly, more that certain actions can have Affinity requirements (which are often not disclosed to the player), and those actions can be vital to starting (or continuing) a given path.
As I said, I think the system is needlessly complicated and is sufficiently opaque that the game is better if you have a guide or walkthrough to keep track of the requirements. YMMV, but hopefully this gives you some idea how it works.
