Within this version of the Fire Emblem Series, two points of speed can literally be the difference between double-attacking a foe or being double-attacked from the opposition. If a unit's speed is just one point higher than that of the unit they are attacking, they will be able to attack twice. This could very well be the difference between life and death in battle.
Speed can be affected by two separate things. The first has to do with the weight of items the unit is carrying. Rings and consumables are weightless, but all other items have some weight to them; shields and stronger weaponry tend to be much heavier. So keep in mind when picking the weapons of your unit as ones that are just a little stronger could stop you from double-attacking, or worse, being double-attacked. Lighter weapons will allow you to keep your speed above the enemy.
The second factor of speed only applies to spellcasters, and it has to do with magic. Oddly enough, each magic spell has a given weight to it, with more powerful spells typically being heavier than weaker ones. As like weapons, attacking with weaker spells could help you gain the upper hand with speed and further allow you to double-attack.
But do note: you cannot choose which spells you counterattack with. Sages and Mages will always counter with Fire, Saints and Clerics will always counter with Nosferatu, and enemy units will usually counter with whatever spell is at the top of their list. Units that can use both magic and weapons work a little differently, as they will attack with their weapons unless the attacker is out of its range. This is very key when your spellcasters are defending and when you are attacking the opposing spellcasters.