Earlier quoted context omitted.
In short: your blood is mostly water. Your blood is surrounded by a selectively permeable membrane (your vascular tissue). Solutes increase osmotic pressure (see: biology 101). Sodium chloride (table salt) is highly soluble in water (see: chemistry). Therefore, sodium and chloride increase the osmolarity of your blood. Water passes through the semi-permeable membrane back into your blood to decrease osmotic pressure…
This explanation, while straightfoward and common-sensical, ignores the possibility that the body has some ability to eliminate excess solutes and/or excess fluids. Certainly the case is quite good that "more fluid in circulatory system yields higher blood pressure."
If this sounds unlikely, understand that the kidney is the direct or indirect target of many medications for blood pressure. Diuretics such as hydrochlorothiazide and loop diuretics such as furosemide act very directly on the kidney. Drugs such as ACE inhibitors (e.g. lisinopril), ARBs (e.g. losaratan), and renin inhibitors (aliskiren) act on the renin-angiotensin-aldosterone system, which directly involves the kidneys in a different manner. (I am a pharmacist).