I've noticed many skills reference a stack of some sort, but I can't seem to find any reference to the stack. Is it simply a counter? Do the stacks increase ever? Here is an in game example.
Defensive Subroutines. You randomly pick a Subroutine
focused on Health or Shields, which grants increased Capacity and
Regeneration for the chosen attribute. The catch? You deal reduced
damage with all gun types. Upon selecting Subroutine you gain 100
Frag Stacks which decrease over time. When you run out of Frag Stacks,
your Subroutine will be replaced with a new one.
Best Answer
Every stack in the game works differently, but there are some aspects in common.
Stacks are gained and accumulate. Each stacks lasts for a while, and then you lose it. You usually get a bonus for each stack. Most stacks will show up on your screen above your experience bar, as you can see in the Nisha screenshot in Chimp's answer. Getting more specific than that requires looking at the specific skill descriptions.
Nisha Example
Feral Chimp has provided a good example of this with Nisha's Order stacks.
There, you can see that the way in which you gain the stacks is spelled out in the skill description:
The skill description also says how you lose the stacks (not included in Chimp's answer):
And also what benefit you gain from the stacks:
and
As well as the maximum number you can have:
Frag Stacks
All the information you need to answer your question is in the skill description you've provided.
How you gain the stacks:
So you get 100 every time a subroutine is selected. This is a bit odd, as most stacks require you to earn them by doing something, such as Nisha's Order stacks which require you to be damaged, or Wilhelm's Rolling Thunder stacks which increase the longer Wolf is active.
How you lose the stacks:
These stacks simply decrease over time from 100 to 0. It's basically a countdown. Although other skills in Claptrap's tree allow you to modify the rate at which it counts down, at first you have no control over it.
What the stacks do:
These stacks are also unusual in that there is no per-stack bonus. Most stacks give you something per stack, like Nisha's Order stacks which give you a chance to heal per stack, or Wilhelm's Rolling Thunder stacks which give extra Wolf damage per stack. Instead, as long as you have Frag stacks you'll get specific preset bonuses to the randomly chosen attribute: health or shields. The bonuses are also listed in the skill: "Capacity +35% Regeneration 2.5% of Max Attribute / sec. Gun Damage -15%". So if Shields was chosen as your subroutine, you get +35% shield capacity, -15% gun damage, and regenerate 2.5% of your shields per second.
How many you can have:
I don't think there's actually a cap on frag stacks, but it might be 100. I'm not really using this tree with my claptrap, except for the one skill you're asking about. Eventually there are skills which let you add to your frag stack total, and it's possible these could push you over 100 stacks. At first though, you can't affect the total, and just get 100 to begin with.
You can see your current frag stack count above your experience bar.