I'm working on creating a half-elf paladin character for a Pathfinder game. Full disclosure: this is the first time I've tried creating a character; I've used ones other people created before. In the text, it mentions something about "favored classes" I believe. What is this?
In Pathfinder, you choose a favored class when you create a character, and every time your character takes a level in that class he or she gets +1 hit point, +1 skill rank, or another race and class specific benefit as added in the Advanced Player's Guide. For example, here's the half-elf's list of favored class level benefit alternatives. See p.31 in the Pathfinder Core Rulebook.
Half-elves have the racial special ability "multitalented" that allows them to select two favored classes.
Let's say you create a new half-elf character and choose favored classes of fighter and rogue. You start off as a first level fighter. You can take +1 hp, +1 skill point, or +1 to CMD vs disarm or overrun. Then at second level you take a level in rogue. You can choose +1 hp, +1 skill point, or +1/2 (a half point, so no bonus yet) to Bluff for feints and Diplomacy for gathering information. At level three, you take another level in fighter. You get the same choices as at level 1 again. At level four you take a level in ranger - you get NOTHING! GOOD DAY, SIR! And so on. I'll also note that if you choose paladin as one of those favored classes, your choices on levelling are just +1 hp or +1 skill point as there's no racial alternate for Paladin for half-elves.
(Minor Addition) With the Advanced Race Guide, which incidentally provides favored class options for all classes(Core Rulebook/Advanced Players guide classes) for all the core races, a Half-Elf Paladin could also gain:
Paladin: Add +1 foot to the size of all the paladin's aura class features. This option has no effect unless the paladin has selected it 5 times (or another increment of 5); an aura of 14 feet is effectively the same as a 10-foot aura, for example.
In D&D 3.5 specific races had specific favored classes, and favored classes affected the rate you gained experience rather than giving bonuses, but that is no longer part of the game in Pathfinder.
Half-elves have the other racial trait multitalented which reads
Half-elves choose two favored classes at first level and gain +1 hit point or +1 skill point whenever they take a level in either one of those classes.
The d20PFSRD says this about favored classes:
Each character begins play with a single favored class of his choosing—typically, this is the same class as the one he chooses at 1st level. Whenever a character gains a level in his favored class, he receives either + 1 hit point or + 1 skill rank. The choice of favored class cannot be changed once the character is created, and the choice of gaining a hit point or a skill rank each time a character gains a level (including his first level) cannot be changed once made for a particular level. Prestige classes (see Prestige Classes) can never be a favored class.
Thus, normally, a creature picks 1 favored class when play begins. The multitalented half-elf picks 2. Then to get a level's worth of favored class benefits, the character must take a level in the favored class. If the character doesn't take a level in the favored class, no benefit is gained.
Unlike most characters, the multitalented half-elf can take a level in one favored class and get that favored class's benefits, then, next level, take a level in his different second favored class and get that favored class's benefits, too. In the latter case, he normally wouldn't get those benefits, but the trait multitalented permits it as it allows a second favored class.
"But I'm Never Multiclassing!"
A half-elf character can trade away the racial trait multitalented for the alternate racial traits arcane training, drow magic, or jungle affinity (and water child if the half-elf also ditches the racial trait adaptability).