Keeping players interested in your world and story is directly tied to how you keep them involved
Get backstories included
First of all, get brief backstories from all your players characters.
They don't have to be ten page reports, just one or two paragraphs that establish a characters goal and some bad guys you could use. Weave those characters into your world and your story.
A lot of new dungeon masters want to create their own world and they never end up using a characters story.
Getting a goal from each character is essential, especially when you need adventure hooks to start a campaign.
Don't try to run all of their stories at once, 5 side quests and a main storyline is a lot for any DM. plan out specific sessions that will highlight one PCs story.
allow players to do some worldbuilding
Let's say you have created your own world, you have mountains, cities, dungeons, oceans and so on. You have areas where different people/races live. This is a staring point for your players.
The players want to be creative making their characters just as you want to be creative when building your world. Include them in the creation process.
You have an elf character? It should be easy to tell your player which area on the map they came from. Or let them choose, and you can create that area on your map based on their history.
Inform your players, let them know where they are from and how they interact with the locations around them, this will let them feel more connected your world.
share the spotlight
Make sure each character gets their turn to talk and role-play.
Most games will have one or two players who lead conversations and make decisions for the group. In most cases this is OK, you need someone to move the plot along and make simple choices for the team.
A natural leader usually emerges that the players will subconsciously follow.
Other times you will get stuck with the power gamer, rules lawyer, or attention seeker who wants to lead the group, but won't actually support the other players.
If your power gamer is trying to do everything, you'll need to stop him. (Isn't it always a "him"?)
The best way to interrupt this is to tell that player to pause and ask what another player is doing at the same time. This is easy during battle when you have to take turns already.
Outside of battle you'll need to control the pace of the story. If someone is taking up too much time, say something along the lines of "While you work on that, let's see what our thief is up to" or "Let's pause for a second and see what the elf wants to do".
This works well when you have an NPC that the players are talking to. If the player job is finding a secret cult, the NPC could say something along the lines of "Do you have a paladin or cleric in your group? I'd rather talk to an expert in the field of religion." The NPC simply won't talk to the attention seeking player.
Create the expectation that players need to share the spotlight too.
give players chances to use their spells and abilities
NPC's or guides in the game can do this for you. "I found a set of foot prints here, is there someone who knows how to follow these?" Or "Looks like this door is locked, is there a talented fellow who could help me out?" and "Does anyone know how to read this scroll?"
You can do this during battle as well, give your magic users and rogues something to do instead of trying to hack and slash the entire session.
Add scrolls for the wizards to use arcana checks. Add puzzles or traps that the rogue could disarm.
This also makes a battle more interesting when you give out goals that are more complex than just defeating enemies.
Prepare obstacles that require specific skills. Do you have a fighter with a really high jump or acrobatics skill? Make sure to add a 10 foot gap that they can jump across.
A rogue with a really high climb skill? Put a treasure chest up on the side of a cliff.
Clerics who have detect poison spell? have the players walk in on a sketchy tea party.
It doesn't have to be a huge part of your story, just a chance for the players to use their skills.
If you have a druid or ranger who can talk to animals, add some creatures that they can talk to instead of fighting monsters all the time.
Every encounter doesn't have to be a battle.
Any given session should have at least one opportunity for some skill check or spell that you know your player has, and is probably waiting to use.
Preparing this way does take a little extra work, knowing what the PC's abilities are, and getting to know what the players like to use.
The extra work is always worth it. It's an amazing feeling when you see your friends do something they've been trying to do for a while. Everyone gets that sense of accomplishment.
control the flow of the story
Good players will always tell you what they want to do before they actually say that they're just doing it.
You have the final say. If you don't say it or allow it, then it won't happen.
When everyone is talking at once and things get overwhelming, stop the group and take one step at a time.
Teach your players that they need to take turns and show support to the others. Establish that in session zero.
If there is a player who hasn't talked in a while, ask them what they think about the situation at hand.
Some people don't want to talk, and that's OK. They will still appreciate that you are including them in the action.
Make sure you listen to all your players and acknowledge what they say and do.
Help out new players.
A lot of new players won't know what to, and it will be your job to help them. It is always OK to give hints, or tell them what you would do as their character with specific abilities.
If you have a good group, the other players will already be helping out.
A good group will let each other take turns talking or making decisions.
As a DM you are the leader and you should be training your players to be working together.
Establish a good group dynamic in session zero. Tell your players that you expect them to help each other out and work together. Especially when you have people who are new to the game.
Remember to have patience for all your players.
If people in your group are gatekeeping or being otherwise unhelpful, the new player might never want to play again. Be as supportive as possible.
it's okay to give players hints
Hints and suggestions are essential for helping out new players, who are most likely overwhelmed by the amount of rules and character abilities.
What do the players know about the bad guys? What do the NPCs know that could help the players?
If you don't tell players what is going on, they will never know what to do.
It is your job to communicate to your players. Let them know what is going on in your world. leaving multiple clues that lead to the same place makes this easy. This helps players make more informed decisions.
Good players should be picking up on your clues and adventure hooks. And sometimes it's ok to help them out.
If you set up a simple riddle or puzzle and they can't figure it out, don't berate them or call them stupid. Be patient. Give them hints. Help them out. Remember it's just a game.
Having fun should be more important than letting your players get frustrated.
If you don't enjoy helping people have fun together, you shouldn't be a DM.
If you aren't patient or adaptive with people, write a book so you can create your worlds all alone.
Have fun and happy gaming!