A Secondary Objective is an item that gives background information and/or context to the mission story, whilst not being of primary importance. E.g. A computer data base that indicates who was carrying out tests or crates that indicates what was being stored at a facility. Finding the secondary objectives will not award victory, as only the primary objective(s) can do that, but can sometimes assist in achieving the primary objective.
The majority of missions feature 1 to 6 secondary objectives, that will reward 5 XP per secondary objective collected with the possibility of 1 to 2 ordnance or in rare cases SP also being awarded. The objectives can be scattered across the map in areas that you won't be inclined to visit or they can be placed close to somewhere you must travel.
The mission objective screen will list the number of secondary objectives present on the battlefield at the start of the mission and does not update when an objective is claimed. The exception is when the secondary objective has a blue mission icon such as the generators to the AA guns in the Drayan Core mission, as this will disappear once cleared. The highlighting of secondary objectives amongst the mission objectives is uncommon.
Almost all secondary objectives are indicated by a teal/light blue shading on the square and are claimed by touching one of the squares it occupies. There are a few missions which don't highlight the SO - Alien Vessel:Bomb Escort (Tact Point); Artifact Vaults (100% collection); Moklumnue Prime: Drop Zone (Xeno Pods) ; Stratos: Defence Relay (Switches - made obvious in other ways). There are others on Stratos that are in need of clarification - Research Hall & Reactor Core.
Usually the objective can be either: a black crate with yellow lid (ordnance), a fuel drum on a tile with red diagonal stripes (hydra ordnance) , a computer terminal, generator or other mission specific floor tile (nothing), or uncommonly a Tactical Point. Do not get drawn into chasing secondary objectives if they require you to take a major detour, as the rewards can be worth far less than a good speed bonus. Instead focus on the main objective and grab any that are going to take 1 Templar 1 turn to claim. Ordnance you find does not carry over to the next mission, so use it.
Escorted civilians & soldiers also award 5 XP per survivor but are not classed as secondary objectives, as they can be lost (die) before the end of the mission, whereas secondaries can't be lost even if the ordnance is used.
Sample profiles of the three different types of Human you will rescue over the course of the game:
Human Scientist (civilian) Level 20: 56HP 4MP 2AP Fortitude 2 Willpower 1 Focus 1 Strength 1 Quickness 1 Warrior 1 Tactics 1 Evasion 1. No talents, cannot attack, does not suffer overheating, can benefit from templar movement buffs e.g. Rallying Charge.
Mariale Throll (VIP) Level 20: 66HP 4MP 2AP Fortitude 3 Willpower 2 Focus 2 Strength 2 Quickness 2 Warrior 1 Tactics 4 Evasion 1 Medic 3; Talent - First Aid 1 (4 Charges) cost 2 AP range 1, single target recovers HP equal to 32 + Medic. Cannot attack, does not suffer overheating, can benefit from templar movement buffs e.g. Rallying Charge.
Human Soldier Level 20: 58HP, 5MP, 5AP, Fortitude 3, Willpower 2, Focus 2, Strength 3, Quickness 2, Gunnery 2, Warrior 1, Tactics 2, Evasion 2. Talent - Semi-Auto Fire 1 (akin to burst fire) range 4, 2AP, 0 Heat, +4 Accuracy, +2 Dmg, +5% Crit chance. Does not suffer overheating, can benefit from templar movement buffs e.g. Rallying Charge.