Sensor Analysis is a passive ability of Federation Science Vessels and Klingon Support Vessels. While maintaining a target selection lock on an enemy less than 10km away, a stacking buff to the vessel's weapons and subsystem targeting will build to a maximum of 10 stack over approximately 60 seconds against that target. Each scan stack adds a 3.33% buff, up to a maximum of 33.3%. Switching targets has a very high chance of removing the buff, so changing targets or having sensors jammed will reset the stack.
It effects Weapon Damage, and Subsystem Targeting Attack "Damage". Meaning if you stay on target the full duration you'll Improve how much damage (after resistances) is done to a subsystem from a subsystem targeting attack, and how much weapon damage your weapons deal. I believe it only effects energy Weapon damage. It could also effect Torpedoes, but I don't believe it does.
You think that your beta test was bad?
Think about this: American Football has been in open beta for 144 years. ~Kotaku
I'm pretty sure it affects all weapon fire, including torpedoes and mines. The tooltip on subsystem powers says it get's bonus, but thats hard to confirm. I do not think it affects science powers like TBR, but I must admit I never particulary looked on that one.