As you've probably guessed, the bigger army you have, the more effective your offense will be, your troops will suffer smaller casualties, and you will be able to keep the public order in your provinces in check. However, a huge army comes with a few problems, which you can read about in the following chapter.
When you should increase the number of your armies?
To simplify things we can agree, that the more numerous your army is, the more effective it will be in combat. While that's not always the truth, as more elite and experienced units are a lot more effective than 19 squads of cannon fodder, it's always better to have a full, 20-unit army than to send your Lord with only a few, even the most powerful units you can afford. Large differences in quantities of armies fighting on the battlefield have a huge impact on the morale. Even the most powerful unit will have its morale crushed and will route when surrounded by dozens of units.
However, the upkeep cost of your army increases as you recruit more units. Every single unit requires a specific amount of gold per turn (this can be checked by hovering over the unit portrait, or by looking on the recruitment screen). To make matters worse, each Lord you recruit (which is a potentially a new army as well) increases the overall upkeep of your army by 5%. Contrary to the previous "installments" of the Total War franchise, in Total War Warhammer it's more affordable to focus on fewer armies while keeping their sizes as large as possible.
When you should be increasing the number of your armies and the troops inside of them? It all depends on the situation on the map, as well as the diplomatic relations between your faction and your neighbors. You should recruit a new Lord (and fill his entire army with even the most basic units) as soon as you start the game. The enemies won't have access to more powerful units as well, and some of the cities (like the capitals of the provinces) are almost impossible to conquer with only a single army, as you have to get through the defenses of the city as well.
Additional Lords (and their armies) should be recruited when you are departing on war with a faction located on one side of the map while the other side is quite vulnerable to attacks from another faction that is hostile towards you. The same applies when it comes to maintaining public order in a province (when, for instance, the land is highly corrupted). Sending an army to one of the cities of such a province will give you a huge (depending on the amount of units in the army) boost to the public order. However, you should use a newly recruited army for such a task - there's no point in wasting high-leveled Lord and his experienced army where it can be done by greenhorns.
When you decide to recruit a large army you must also remember about keeping the income of your country on a decent level. 1500-2000 gold per turn is an absolute minimum - having less (like, for instance, 500) gold per turn won't allow you to develop your settlements. After several turns of such stagnation your enemies will have access to more powerful units.
Casualties can be replenished using different methods. The first and probably the most used is to, basically, allow your troops to "rest". When your army is located on a terrain belonging to your faction and the terrain is suitable for your army (more on that can be found in the World Map section), your troops will replenish a portion of their casualties each turn you spend there. The speed of this process can be increased by using a specific marching method, or by entering your own city. Additionally, the replenishment rate can be further augmented by constructing specific buildings in the cities inside of a province your Lord is, as well as by picking certain abilities with your Lord and Heroes. The amount of turns required for the unit to completely recover can be checked by hovering over the "cross" icon located in the lower right corner of its portrait.
Another replenishment method requires you to pick up a specific option after defeating an enemy army in combat. It can either by capturing and forcing enemy soldiers to join your army, dominating them (with Vampire Counts), or even eating them (with Greenskins). This way you will be able to instantaneously replenish even up to 15% of total casualties, without having to pay anything for it and spend precious time recovering. This method has some limitations - you won't be able to use it after defeating a faction that is of a different race than yours (Dwarves won't magically turn into Humans, and the troops of Vampire Counts into Dwarves).
The last method is to merge several wounded units into one. If you have, for instance, two units that have 40/80 troops inside of them, you can merge them to turn them into a single unit with 80/80 troops. All you have to do is to hold the CTRL key and highlight the units you want to merge with your mouse. Afterwards, you must press the specific icon that will appear when you hover over the portrait of any selected unit. This method allows you to get rid of severely wounded units that take forever to recover and quickly recruit new troops for their place. This is by far the fastest method of replenishing troops, but it's also the only one that requires you to use gold (to recruit new units).