I think the DM has three tools at his disposal to further immersion:
The first thing you need to do is creating a world that is interesting and just begs interaction. Even on a pre-created adventure path, you can introduce a lot of sandbox elements - and even in a pure sandbox campaign, your goal should be to have powerful story emerge from the seeming randomness. Make sure the individual elements of your world don't only function on their own. The key to successful world-building is interconnecting the various bits and pieces into a collective whole. The more interconnections you weave between the phenomenons, structure, and actors in your world, the more your players will feel as if they're just a part of something bigger. I have a looong post
here where I detail how this can be done. It's concerned with somebody's asking about the 3E Red Hand of Doom campaign, but I think you might find something interesting there for other campaigns, too.
The second part is making sure you do good descriptions. Remember that PCs only interact with the game world via your describing it. So working on evocative detail, getting the words just right etc. are important. Moreover, you can use a variety of simple tricks to give the impression that there's more, everywhere around the PCs, than you have time to describe right now - but if they go off and explore, there'd be a living, breathing, ready-made world just at their fingertips. I discuss a few techniques
here, if you're interested. These are mostly limited to making a city come alive, but can easily be adapted to other settings, as well.
The third bit is populating the world, i.e. the skill of inventing and impersonating interesting NPCs. This really comes down to your acting skills and your empathic creativity, and others have been over this time and again, better than I could break it down. Have a look
here, for example, but searching this board should turn up a lot of good threads as well.