Your steps make no sound when walking
There is no division into rules and fluff text in spells or magic items in 5e, it's all rules text.
The straightforward mechanical effect is Advantage on Stealth checks. But there could be others, for example there could be a glyph of warding set to trigger when someone walks by, making a sound. The owner of such boots could want to set that condition on it.
The "also" clause makes it so that advantage on stealth checks is always guaranteed, and not dependent on DM adjudication, unlike other effects of stepping silently. (Thanks, @Pepijn).
From a pure rules-as-written perspective, spells and magic items only do what they say, so strictly read, the boots do not protect you from tremorsense, as tremorsense triggers on vibrations, not on the sound the vibrations would maybe make.
A monster with tremorsense can detect and pinpoint the origin of vibrations within a specific radius, provided that the monster and the source of the vibrations are in contact with the same ground or substance. Tremorsense can't be used to detect flying or incorporeal creatures.
Again, it does not say they don't detect creatures that make no sound when moving.
Now from a physics perspective, it is impossible to not make a sound when causing vibrations, at least in the material you vibrate, because sound waves essentially are vibrations traveling through some medium. But D&D is not a physics simulation. There would be other consequences that are more obviously outside the scope here: for example, when you apply pressure on a material, then remove it, that will cause it to move, and the vibrations of that movement will create some kind of (however hard to perceive) sound. Does that mean the wearer of those boots does not cause pressure and can walk over snow, quicksand and water? Surely not.
That said, we in our group house-ruled that the boots do protect from tremorsense, as it sounds so intuitive, and this has not caused issues. It has slightly improved the power of this non-attunement item, and has helped cause some cool moments, for example where a thief could walk by a corridor undetected while an earth elemental was on the other side of a door to guard it, and it also helped in a combat against Umber Hulks.