Aravind, As you can see from the answers and comments you have opened Pandora's box [look her up]. What you have astutely inferred at an early age is that textbooks, teachers, the internet, and everything are incomplete in explaining anything. I will try to explain acids and bases in the manner your text tried. Remember this is to describe the acids and bases you probably encounter daily or occasionally not the chemical and physics reasons that there are acids and bases. First! Every substance likely to be encountered is made of atoms [except possibly a lightning bolt or electric shock they are made of electrons, but the electrons came from atoms and are trying to get back to atoms, it is prudent to not get in their way.]
The common properties of acids and bases involve water and aqueous solutions but are not limited to water. We will stick to water and aqueous solutions. Water is both an acid and a base for 2 reasons The first is that it reacts with itself to form very small amounts of H3O+ and OH- ions, 2H2O = H3O+ + OH-, and second because water can donate protons, be an acid, or accept protons, be a base. We have established that an acid in water is either a solution of H3O+ ions [commonly called hydrogen ions or H+ ions] or is a compound that can possibly donate protons to a base. A base is a compound that either forms hydroxide ions in water or can accept protons from an acid.
There are two main classes of acids and bases. The first is Strong; these react completely with water and are essentially solutions of H3O+, acids; or OH-, bases. Common strong acids are hydrochloric-HCl [stomach acid], nitric-HNO3, Sulfuric-H2SO4; common strong bases are Sodium hydroxide-NaOH, potassium hydroxide-KOH, possibly calcium hydroxide-Ca[OH]2. The second are the Weak acids and bases. These only react partially with water to give hydronium or hydroxide ions. Some weak acids are acetic [vinegar], citric [lemon, orange juice] lactic [sour milk, yogurt]. Some weak bases are bicarbonate ion, HCO3-; Ammonia, NH3.
Acids and bases react to give water usually leaving the counter ions in an almost neutral solution. Removing the water results in a compound called a salt. the term comes from common table salt NaCl that can result from the reaction of NaOH and HCl. Salts usually dissolve in water as ions Positive ions from the base and Negative ions from the acid. Some common salts are Sodium chloride NaCl common table salt, Ammonium chloride NH4Cl found in cough drops, sodium bicarbonate NaHCO3 baking soda, sodium carbonate Na2CO3 washing soda, sodium hypochlorite NaOCl bleach, Calcium carbonate CaCO3 limestone, marble, chalk, Tums antacid. Salts are everywhere.
Common acids: Stomach acid-hydrochloric, acetic acid-vinegar, oxalic acid-spinach and other greens, Citric- lemons oranges fruits, lactic-sour milk, carbonic soda water rain water. Some common bases: sodium hydroxide-lye drain cleaner bleach, Ammonia- some cleaners, bicarbonate ion-baking soda antacids, Carbonate ion-washing soda.
Acids, bases, salts, And Chemistry are everything about you. Observe, ask questions and look for answers. Best of everything.