Changing any of your units' classes is sort of unnecessary to beat the game, but you want to use all that you can get. There's no reason not to throughout most of the game.
As you may already know, the Master Seal is an item that promotes units of a basic class to an advanced class. In most cases, the unit has one or two classes to choose from to promote into. Their level is reset to 1 and they may resume going back up to 20 to continue gaining stats and learning more skills respective to that new class. This is how they become more powerful.
The Second Seal can do the exact same thing as a Master Seal, except more options are given to the unit, and in some cases, the Second Seal is the only option for units to change classes. This is especially true for classes like Villagers or Dancers because they have no classes they can promote to, or a unit that has already reached the limit of their advanced class. Master Seals wouldn't work here. The main purpose of a Second Seal is to allow a unit to essentially "begin anew" (ergo, there is no limit to how long you can level your units) or take on a completely different path not native to his or her default promotion tree. What classes can be accessed with a Second Seal depend on both the individual character and their level.
Suppose that Chrom is a Level 20 Lord. A Master Seal would change him to Level 1 Great Lord. A Second Seal also does this, but also allows Chrom to become a Sniper, Bow Knight, Paladin, or Great Knight at Level 1. This is because Chrom has the ability to go down the Cavalier or Archer class trees with the Second Seal. Within any advanced class before reaching Level 10, Chrom may use another Second Seal to "demote" back to the aforementioned classes' base classes, including his original (Lord, Cavalier, or Archer). He can still do this when he is over Level 10 in his advanced class, but now also has the ability to change his class to his other advanced classes as Level 1, like going from a Level 16 Bow Knight to a Level 1 Great Knight.
Changing a unit's class to another class tree is known as reclassing. The incentive of reclassing is to learn the skills unique to every class, so that you can optimize your unit's potential in combat, but more importantly, reclassing allows an infinite continuum of leveling for all units. If your unit stops getting experience and they can't promote, throw them a Second Seal so that they can keep on growing and getting stronger.
