Three main factors converged to produce the modern continuous front. They were 1- the size of armies, 2- the firepower of modern weapons, and 3- the nature of logistics.

The armies of WWI were immense on a scale difficult to fathom. The German army alone counted 4 million men in 1914; perhaps 20 million were under arms around Europe. It's only natural that a large army will occupy more space than a smaller one.

Moreover, the greater firepower of 20th century armies allowed and indeed compelled men to spread out more. In ancient warfare, men fought close together because their weapons could only reach arms length; if someone tried to stab your comrade, you had to be right next to them if you were going to try to stab back. With quick loading artillery, machine guns, and repeating rifles in mass use, men could support each other from farther apart, which also left them less vulnerable to enemy firepower. Fewer men could thus hold more space, but these weren't armies of fewer men, so it was more men and even more space. The deployed frontages of units came to surpass the space between them on the march, thus allowing more to be kept in reserve, preventing the enemy from easily piercing an extended front.

Lastly, the nature of logistics. Armies of the 20th century had to rely on a forward shuttling of supplies, because the vast bulk of their requirements -ammunition, fuel, spare parts, etc- had to be made in specialized and centralized factories. You can't extort the French villages along your line of advance for 20,000 105mm shells, after all. Modern warfare consumes staggering quantities of ammunition and fuel, so armies need to make periodic stops to restock; it's easier to move supplies forward to stationary forces than those on the move. This gives the armies time to more fully deploy and cover more of the porous front that develops during the advance.

None of these conditions which give us the modern continuous front apply to warfare before the 20th century.

Even the armies of the Napoleonic Wars, so vast compared to everything that came before them, were never so big as to stretch from one impassable obstacle to the other in battle order. In order to not be broken through, 10,000 men per kilometer was probably average on the Napoleonic battlefield; even an army of 250,000 would thus only occupy a front of 25 km.

When armies attempted to guard wider fronts than this, concentrated forces tended to easily break through; in the 18th and 19th centuries, this was called the 'cordon system', and has been much maligned since. While the army on the wider front could theoretically envelop the more concentrated force, the distances involved were great enough and defensive firepower weak enough that the concentrated army would defeat the meagre forces in front of it before any threat to its flank became relevant. A good example of this is Bonaparte at the battle of Borgetto, in which the Austrians attempted to defend every river crossing in the 31 km between Lake Garda and Mantua with 20,000 men. This position was only a day's march across, but that was still plenty of time for Bonaparte to defeat the small force guarding the crossing at the selected point.

I hope this explains why armies were not always getting surrounded; their size and the limits of firepower imposed limits on the frontages they could effectively occupy.

So would Armies just like “meet up” in a single area to fight? Why would they do what they did?

They usually didn't arrange battles by mutual agreement if that's what you're picturing. Rather, an army intent on fighting a battle would either track down and advance on the enemy army, forcing them to either fight, withdraw, or remain in a fortified camp, or they would undertake some action to bring the enemy army to them, such as besieging an important place or laying waste to enemy territory. Armies sought to fight battles because winning one typically let them pursue their objectives (such as taking territory) without another army in their way.

Another army can just go around them on either side

One problem is that there were limits on armies' mobility; they needed roads for their wagons, artillery etc., and good roads were not as common before the modern period as they are now, so there may not have been an easy alternate route.

Another problem is that most useful invasion routes for a country tend to have fortresses guarding them; if the invaders don't leave behind substantial forces to blockade them, the garrisons, to say nothing of the defending army, can block supplies from the invaders' base from reaching their army in the field. This would make it almost impossible to conduct a siege, as the besieging army would quickly exhaust the supplies available nearby. Because wars were often fought for territory, taking fortresses was often the critical part of the war, as you can't gain much revenue from a territory with a hostile fortress planted in the middle of it. You usually can't besiege a place in hostile territory without leaving behind substantial forces to keep your supply line open, thus leaving you weaker against the enemy army. Often it was better to face the enemy army with your full strength from the get-go.

That said, it was certainly still common for armies to spend weeks evading each other when there were good roads available and not too many fortresses guarding them. Most campaigns tended to be ones in which neither side sought a decisive outcome from battle. Still, 'going around' the enemy army wasn't a silver bullet, since there are definite limits to what an army can accomplish while a strong enemy force is still in the field.

I know this is a pretty general overview, so please hit me with any follow up questions or specific instances you have in mind.