An acid is a substance that can donate a hydrogen ion (H+) (generally speaking, this will be a proton) to another substance. Acids have a pH less than 7.0. A chemical can donate a proton if the hydrogen atom is attached to an electronegative atom like oxygen, nitrogen, or chlorine. Some acids are strong and others are weak. The weak acids hold on to some of their protons, while the strong acids let go of all of them. All acids will release hydrogen ions into solutions. The amount of ions that get released per molecule will determine if the acid is weak or strong. Weak acids are acids that partially release the hydrogen atoms that are attached. These acids, then, may lower pH by dissociation of hydrogen ions, but not completely. Weak acids generally have a pH value of 4-6 while strong acids have a pH value of 1 to 3.
A base is an acid's "chemical opposite." A base is a substance that will accept the acid's hydrogen atom. Bases are molecules that can split apart in water and release hydroxide ions.