All names are symbols. Symbols point to or refer to other things, people, events, ideas etc. A written or spoken name in any language (including sign languages) refers to a thing which all people who know that language recognize; so symbols are culture and language specific. Interpretation of a symbol depends on the background of the person who says it and one who hears it. (Example: Swastika to a Hindu is a holy symbol but to a person with Jewish background it represents Nazism. A cow represents Shri Krishna to a devotee of Krishna, but to others it reminds them of a hamburger!).
Also, symbols depend on the context in which they are placed. (Example: A cross on a building point to a church, but a cross on ground means it is burial place, and a cross on an answer-sheet of a student means a wrong answer!) Hindus and their scriptures emphasis again and again, that the real you is the same in essence as the Supreme Being (Tat Tvam Asi), hence, all practices of rituals, pooja, worship, prayers and meditation, yoga, mantra, Vedanta, social work, etc. are developed with a view of helping human beings to go beyond the belief and actually realize that oneness with the Supreme Being( or God by whatever other name one chooses).
Hindus worship one supreme reality (God) but in many forms, or no form, with various attributes of these forms. These deities represent various aspects of God's powers and qualities etc. A better understanding of these forms, decorations on them, things held by them in their hands, things around them, their vehicles etc. will allow us to connect better with these deities, and help us advance in our goals. Ultimately, when thoroughly understood, we realize that these are the powers and qualities hidden in our own self, of our own real self (Atman). By proper control, training and practice of Prana, mind, body and intelligence we discover our own self.
These forms in pictures or temples can be interpreted in many ways depending on one's shraddha, one's religious tradition and mental makeup. Persons following different paths (of knowledge, devotion, action, mind control etc.) will have different meanings attributed to the symbols which is perfectly acceptable as long as it helps one to progress. Typically, there is an ordinary or traditional interpretation and also a deeper mystical/spiritual interpretation. Which is the correct interpretation? That which helps you progress spiritually and makes you a better human being is the correct interpretation for you.
People do not worship idols, icons, picture or statues. They use these to focus their minds upon higher, nobler qualities and cultivate them, or to cultivate mental powers to overcome negative qualities and habits.
Just as a flag arouses thoughts of patriotism, so does an image arouses qualities represented by that image. The idea of 330 million gods is only a metaphor for innumerable ways one can imagine/superimpose only a few of infinite qualities represented in each form of God. These gods are not independent and rival powers but are aspects of the one Supreme Being. This short pamphlet gives a brief explanation of some of the popular deities worshipped by Hindus. We hope it will be useful to you when you pray or meditate on these deities.