Local Tax Modifier vs. Local Tax Value in Production Interface

What is the difference between Local Tax Modifier and Local Tax Value, along with Production and Manpower, in the Production Interface?

Local tax value consists of the base tax (which you can influence by development with the common sense dlc) and added tax value from buildings. In the current version of the base game, only the native building longhouse adds tax value, however mods often make use of this.

Tax modifier is simply a bonus to the tax efficiency, which is multiplied with the base tax.

E.g: a province with 5 base tax, which is a core has 100% tax efficiency and thus will yield 5 ducats per year in taxes. If it's blockaded, the tax effiency falls by 75%, so the province only makes 1.25 ducats per year (or a bit over 0.1 per month). Building a temple increases the tax modifier by 40%, bringing tax efficiency to 140% or 7 ducats per year and 65% (3.3 ducats per year) when blockaded.

Production is similar. Each province produces a certain good. Base production is how much of this good is produced (and can be increased with development), this is modified by production efficiency. Multiply this with the trade value of the produced good (this depends on the global market, but generally remains within certain constraints, e.g. silk is always valuable) and you get the production value, which is the yearly amount of ducats gained from production in this province. Also keep in mind, that the produced trade goods will play a role in trade.

Manpower finally determines how many possible soldiers this province provides. It is added to a global pool, from which you can recruit regiments. Higher manpower gives you more of a buffer before your war machinery screeches to a halt and also regenerates the pool faster. Again, you have a base manpower provided by development, which is modified by the efficiency value. Sailors are very similar, they are basically the manpower for your ships.

Efficiency can be both local and global and is added up. Global affects all provinces, local only the province it occurs in (usually buildings provide local modifiers).

Finally, keep in mind that all those values get negatively affected by local autonomy. Each 1% of autonomy reduces the total production of all of the above by 1%, e.g. a province with 80% local autonomy only produces 20% of what it would at 0% autonomy.