So I was trying to figure out what Opportunity did as well, with some testing I think I've got a bit more insight into what's going on with this ability.
Ignoring the meter mechanic for starters, the information in the inherent description about defense and resistance appears to be correct. All primary attacks appear to inflict a 3.75% defense debuff and a 5% resistance debuff on targets hit. This does not stack from the same sentinel, whether by repeated uses of one power or uses of different powers. The inherent description suggests it can stack from different sentinels; this would bear some testing. The debuff amounts are affected by the purple patch, so they are smaller against enemies higher level than you and larger against enemies lower level than you.
As for the meter mechanic, attacks from the primary (plus brawl) increase the bar by an amount that more or less depends on the recharge of the attack. (The character I tested this on doesn't have any pool attacks to test, so I don't know if those count.) From the attacks I have available to me the increase seems to be roughly equal to base recharge plus about 4-6; the increase is consistent over multiple uses of the same attack but the bonus amount seems to follow a slightly different formula for different powers. (Brawl (2s): +6.73, Power Bolt (4s): +7.92, Power Blast (7s): +12.61, Power Burst (10s): +14.92.) AoE attacks seem to have the area factor divided in, though again the formula isn't exact. (Energy torrent (12s, area factor 2.38): +8.41.) AoEs do *not* give more bar if you hit more than one target - the amount is fixed. The amount gained appears to be set by the *base* recharge, as it did not change after slotting a recharge enhancement.
If not used the bar decays, though quite slowly. In my testing it took a couple seconds more than 2 minutes for the bar to decay from 100%-0%, for a decay rate of about 0.8 units/sec. Interestingly enough, the decay seems to be paused while in combat - both enemy attacks against you (hit or miss) and your attacks against enemies seem to pause the decay for a few (4-5ish) seconds.
Once the bar is above a certain threshold, which seems to be 90% from my testing, your tier 1 and tier 2 attacks gain the ability to set off your Opportunity inherent. This is indicated visually by a red ring around the tier 1 and a green ring around the tier 2. Successfully hitting (missing doesn't count) with your tier 1 activates Offensive Opportunity, and hitting with your tier 2 activates Defensive Opportunity, both for a duration of 15 seconds. When triggering either type of opportunity, a large targeting reticle graphic will appear under the feet of the enemy you attacked. This represents a 20% resistance debuff placed on that target, which lasts for the same 15 seconds. Like the resistance and defense debuffs from the base inherent, this debuff is affected by the purple patch.
Offensive Opportunity causes your attacks to gain a bonus tick of damage. This bonus tick applies no matter what target you are shooting, and seems to be equal to about 18-20% of the attack's damage (consistent across multiple uses of the same attack, but varying slightly between different attacks). Interestingly enough, this bonus tick of damage appears to ignore damage buffs, as it was unaffected by slotting a damage enhancement or using a red inspiration. It does, however, increase as usual with resistance debuffs on the target
Defensive Opportunity causes your attacks to heal you for an amount equal to roughly 26-27% of the attack's *base* damage. This seems to be independent of the damage actually inflicted on the enemy - it does not vary when slotting damage enhancements or using a red inspiration, and it also does not vary when attacking targets of different levels or under the effects of different amounts of resistance debuffs.
The combat log also indicates that attacks under Defensive Opportunity also restore some amount of endurance, but does not report the exact number. Anecdotally, when watching one's endurance bar while attacking one can see that the bar does drop and then immediately bounce back up, but it is difficult to tell by exactly how much. The endurance recovery amount seems to be less than the endurance cost of the attack, but still quite significant. More testing is needed to determine what controls the amount of endurance recovered.
Whether the percentages of bonus damage, healing, and endurance recovery changes based on the level of the user is unknown. The majority of this testing was done on a level 8 Sentinel; at the end of the test I allowed myself to level to 9 and then re-checked the bonus amounts and did not see any significant changes in the percentages, but even if the amounts do scale one level may not be enough to cause a noticeable difference.