Fabric with a denser weave feels smoother. Rub the fabric between your thumb and forefinger .. can you feel the weave of the fabric with your thumb, or does it feel smooth?? As an example of two opposite ends of the spectrum but the same principle ... silk charmeuse compared to burlap. You can obviously feel the weave of burlap, you can't feel the weave in the silk. Sometimes washing/drying will shrink the weave and pull it together more and the feel will become softer - but I would rather not take the chance that it won't improve enough.
Also ... look for obvious "slubs" which are thickness variances in the fibers. You see it in a lot of organic fabrics to some degree, even in blue jeans ... ever see a small single piece of thread that is clearly thicker than the others around it? That's a 'slub'. An occasional small slub is forgivable, but they shouldn't be frequent or large.
Lastly as others have mentioned, hold it up to the light. How much light shows through? Sometimes with cheaper fabrics you will even see dots of light penetrating through where the weave intersects!!
You'll hear quilters and garment makers refer to a fabric having a "nice hand". This is (part of) what we're talking about.