There are many things that can cause that, usually a result of normal wear & tear and likely its still fine to drive normally but if you expect to keep it around a while there are some things you could look into to refresh your engine.
This is going to be just very general advice because I don't know the miles on your vehicle, your driving habits, its service history, etc.
Before getting into engine parts lets touch on motor mounts
. The healthiest of engines can shake around and cause what you are describing if one or more motor mount is wearing out. The engine is not rigidly bolted to the rest of the car, big blocks of glorified rubber are used to isolate engine vibrations from the chassis but if they wear too much they can allow the engine excessive movement. It doesn't actually take a lot of play to enable a shuddering or clunking due to bad mounts.
Likelihood: Some people can drive cars to 300,000 miles and never wear out the motor mounts. Its mainly dependent on your driving style, how hard and often you take off quickly from stops and such. Some vehicles have been known to have faster wearing mounts than others too so even a Grandma *could* end up needing to replace them depending on the vehicle but not knowing you its hard to say. They are relatively easy for a mechanic to check but they often don't bother to inspect them unless you ask them to or they are bored and looking for things to add to your bill.
So, engine to chassis connection is one possibility. Most everything else deals with the health of the engine itself.
First and foremost, have you even checked the oil level? To be clear, low or dirty oil is almost never the cause of the problem the real reason I always ask that first is to find out if you have any ambition whatsoever. You should be checking the oil regularly.
Moving on, you didn't describe the service history or how many miles so pertinent questions for a rough idling engine would be
1) Is the air filter dirty? Has it ever been replaced?
2) When was the fuel filter last changed?
3) Has it ever gotten a fresh set of spark plugs? (and if applicable, spark plug wires)
4) Are all the coil packs working well?
5) Is the PCV valve clean and working?
6) Is the throttle body and/or mass airflow sensor gooped up with soot, oil, etc?
7) Are the engine vacuum levels within spec? (or at least do a general check for a vacuum leak)
Some much less likely ones that have gotten me in the past:
Is the battery in good shape?
9) Is the alternator working well?
Like I said, not likely but occasionally an electrical gremlin will cause all kinds of weirdness.
Usually an engine that runs but runs a little rough or isn't getting its best mileage is due to a minor problem with fuel, air, or spark. The above are the somewhat reasonable things a guy can often check and replace himself. After a certain point of high mileage the same issues can also be from lost compression do to worn piston rings or dirty fuel injectors or other much more involved issues of wear and chances are you are not equipped to deal with issues like that, if you were you wouldn't be here asking what it could be.
You may be tempted to drop a bottle of fuel injector cleaner in there just as a $5 shot in the dark and that would be fine. 95% of the time those bottles of "cleaner" don't do diddly squat but since its not feasible for you to pull out the injectors and clean them for real it can at least make a person feel better sometimes. Just keep in mind your brain is going to want to believe very badly that you can "feel" some difference after putting a bottle of magic cleaner in the gas tank, don't read too much into that just know your impression is going to be skewed because you want to believe you did not just throw $5 away for nothing. Don't go cheap on the fuel injector cleaner, use name brand and use their "good bottle". That may set you back $6 or $7 and make you want to believe even more that you feel some "improvement" that is likely not there but just take it with a grain of salt and give it a try. Put the bottle of juice in first on a low tank and then fill with gas so it mixes better.
I would not recommend seafoam, personally. You read a lot about it and there are some interesting videos but its just smoke from burning the product. You see a video of an old car rolling coal like a diesel and they say "wow look at it disolve and burn that carbon off!" but then if you search you find people putting seafoam in brand new (clean) engines and getting the same smoke so... its not carbon burning off, its just the product.