While in the overworld of Mount & Blade II: Bannerlord, each party is represented by a single leader moving across the map. There is the fast-forward button which helps longer travels be accomplished much sooner. While the fast-forward button speeds your character up, it also speeds everything up, and the differences in speed between you and other parties are still clear.
Having a faster movement speed will help you outrun stronger enemies should they be chasing you. If a faster party chases a slower one, there is little that can be done to escape a persistent foe. On the other hand, many easy targets you may be chasing down have a better chance of outrunning you and escaping with valuable loot.
What Effects Movement Speed
Your movement speed is affected in small amounts by multiple factors, simply being better about one way may give you a small boost but won't result in a noticeably faster movement speed. These factors include your party's size, the weight of what your party is carrying, prisoners, the number of horses, the terrain, whether it is day or night, and individual perks and skills. Should you also be leading a very large army, speed is out of the question, and you'll be walking to whichever castle is your target.
All parties in the overworld move slower during nighttime. This is unavoidable, but does affect everyone equally, and shouldn't affect a chase that went into the night. Other terrain elements also affect your speed such as moving through a forest instead of a flat plain. Should your character be of Battanian origin, the forest effect is slightly negated, otherwise these effects or unavoidable.
Speeding Up Your Party
Your party's speed is heavily influenced by the number of troops walking in the party. As you get more troops, your party will slow down due to the number of units. While cavalry units help your movement speed, infantry units' movement speed can be countered by having extra horses in your inventory. Horses come in two types, speed or beast of burden. Having many extra speed-type horses in your inventory can greatly increase your movement speed, and your goal should be to have as many horses as you have party members. This benefit also applies to cavalry units as they ride speed-type horses.
Having many prisoners will also slow down your party, so it's best to ransom them at the nearest tavern or recruit them into your own party. While there is a limit to your carrying capacity, the more items you have the slower your party will move, even if it's well below the carrying capacity. It's best to constantly sell unused items at the nearest merchants to help keep your party fast.
There is also the final skill of the Scout tree, Uncanny Insight. This skill increases your movement speed by .1 % for every skill over 200. While this bonus seems insignificant and difficult to get, it is very worthwhile to get in the late game when you have many skills maxed out. Along with focusing your party's inventory and makeup to prioritize movement speed, this skill will only further the bonuses. In the campaign settings menu, there is also the option to increase your parties' movement speed while not affecting others in the world.