Substitute characters are a set of playable characters that appear in Fire Emblem: Genealogy of the Holy War. They appear in the second generation if some of the female characters from the first generation were left unpaired or died before reaching the end.
They are called substitutes because they take the place of the corresponding children characters of the second generation. Their role in the story is essentially the same as the children characters and they have similar or identical dialogue and events (although some substitutes have extra hidden events, such as Laylea obtaining the Barrier Sword). However their names are different and their appearance is usually different from the children characters. They also have fixed base stats, growth rates, equipment and Skills.
While the substitute characters have different and sometimes inferior stats to the children characters, the extreme dislike by many fans might not be completely warranted in all cases. In reality, not all of them are necessarily bad: in example, Teeny's replacement Linda has rather high magic and can get to use the Thoron tome, Corpul's replacement Sharlow's stats are more balanced than Corpul's in addition to the Elite skill, and Hawk is a rather decent character on his own (with Ced's biggest advantage being inherited items like Forseti or Valkyrie, which can also be obtained by other characters fathered by either Lewyn or Claud.)
On the other hand, while not being bad, they do have genuine disadvantages compared to the original children. First of all, they are not as customizable as the 2nd generation children, due to their aforementioned fixed stats. Second, the stats of second generation children are affected by the final stats of their parents, meaning that most of them have the potential to be quite better than their substitutes. Third is that some of the children can use legendary weapons and spells, which the substitute children can't due to their general lack of holy blood - and the two children who do have a heroic lineage, Amid and Linda (minor Tordo), are unable to use the holy weapon associated to their heritage (the Mjölnir).
(Interestingly, this is alluded to in-story, since several of the substitutes are painfully aware of their disadvantages - like Mana, Dimna, and Asaello).