Having high loyalty in a region will provide better intelligence on enemy moves in the region and in those adjacent to it, but not as much as if you have good scouting units like cavalry and partisans. Also, regions that are very loyal to you and are enemy controlled, but that are not garrisoned by enemy troops will gradually revert into your control. Military control represents small combat units actively patrolling the region and their control of the land (this function is handled by the game and does not require the player to do anything other than leave troops in the region to gain more control percentage). Last, but not least, you will want to have the highest loyalty possible in your production regions, because people have to be on your side to sustain the war effort.
On the other hand, you will have trouble in areas which are not loyal to you. Partisans can appear, cities that you hold without a garrisoning unit can switch sides if there is unrest in the region the land (90% or more loyalty for the other side) and local people will gather & forward information on your moves to the enemy!
What are your options for counter-insurgency? You have many. On the local scale, you can keep a significant garrison in the region, to progressively suppress the activists (backed by a leader with a bonus in suppression, if possible, like Butler in New Orleans). Or you can focus your armies on taking most of the strategic cities of the state, thus disheartening your foe: this will reduce how loyal the population is to him in this state.
Finally, you can act on the state level, by tweaking the Domestic Policies screen! This screen let you decide, state by state, how much you restrict the individual liberties of the population. You can choose between Normal Rights, Suspend Habeas Corpus or Establish Martial Law. Depending on your choice, the loyalty of the people in each region of that state will start to gradually shift. Note that there are bad points to some policies though. For example, the restricted liberty policies will cost you Victory Points, and harsher policies will lower the population's loyalty in a region faithful to you even as they keep the malcontents in line.
