Sous vide cooking has three essential steps which make it different to regular cooking:
- Long-term low temperature precise cooking (you need appropriate kitchen appliances to do this)
- Bagging the food you're cooking (with a plastic or silicone bag or some kinds of cans)
- Vacuuming the bag
The bagging is to avoid osmosis. All biological cells have a lipid bilayer which gives these cells a semipermeable membrane. That means as soon as you submerge biological cells into water, osmosis starts to equalise the water concentration on both sides (sides referring to your water bath and whatever you put into it).
An example of this is a normal soup. By putting vegetables in it, they will soak with water (due to osmosis) and get a little bit softer. In the process of this, the original structure of the vegetable in question is changed and so does its flavour. In soups, this is what you want to do. You want some chewy bits of vegetables, meat or anything else but you also want that the broth you use taste differently than plain water. The flavour is diluted.
With sous vide, you don't want to have this. You want to retain the original flavour so you bag whatever you're doing. This is especially important for meat and fish as both taste considerably different when soaked with water. So putting meat into your water bath without a bag will lead to the meat soaking itself up with water - now you have a watery piece of meat which tastes great in a soup but if you're not preparing a soup, the taste is off.
Vacuuming your bag isn't really a strong requirement expect if you truly want to have everything perfect. Vacuuming is all about thermal conductivity as you already noted. (But not in the sense that a vacuum can transfer heat especially well, actually it's a perfect insulator for conduction and convection while radiation is still possible.)
In sous vide cooking, heat is transferred primarily through conduction: Your food is in direct contact with the plastic bag which is in direct contact with the water. Little air pockets within the bag hinder a perfect conduction of heat so your food is unevenly warmed. That's the reason why you would want your bag to be vacuumed: to get an evenly heated surface.
My personal experience is that a perfectly vacuumed bag is nice to have but not absolutely necessary - the step from frying your food to preparing it via sous vide already makes a considerable difference in taste, structure and optical appearance even if it's not vacuumed. Vacuuming provides the final touch.