A focus and specialization feat tree is used to make a character better at two aspects of a particular ability. These improved abilities apply to a subset of items the character is proficient with, such as a particular type of armor, a particular type of weapon, or a particular school of magic.
Feat trees of this type generally follow a common pattern.
Focus feats in such a hierarchy generally provide a ‘+1 or -1’ benefit, perhaps equal to one level’s worth of ability. Weapon Focus provides a +1 bonus to attack rolls with the chosen weapon type, School Focus provides a +1 bonus to caster level when casting spells of the chosen school, and so on.
Specialization feats in such a hierarchy generally provide a ‘+2 or -2’ benefit that works against an opponent. Weapon Specialization provides a +2 bonus to damage done with the chosen weapon, School Focus increases the save DC of spells from the chosen school.
The feats are usually available in alternating order, at levels 1, 4, 8, 12, 16, and 20, as shown in the feat hierarchy. In a core rules game the feats may be limited to specific classes. Most of the Weapon Focus Feats may only be taken by Fighters, Armor Focus Feats likely would be, School Focus Feats might be limited to Wizards only, and so on. I do not have these limitations in my campaign, anyone who meets the (level-based) prerequisite — Base Attack Bonus, caster level, and so on — may take the feat.
These feats may have other prerequisites or limitations. For instance, Armor Focus Feats are limited by armor type (Improved Armor Focus works only with medium or heavy armor and Greater Armor Focus works only with heavy armor; lighter armors do not provide enough protection to take advantage of).