Pentagram and pentacle are virtually the same purpose, protection and also usable as a focus for other spells.
Hexagram is similar, enough so to be used the same way for most things.
Triquetra is a wiccan symbol (I believe) which probally represents the triple goddess or the states of maiden/mother/crone that makeup the functions of the goddess aspects.
These are off the top of my head at 2 am, so pardon any inaccuracy. Ppl are mentioning to use google because if you search yourself instead of getting the info Handed to you the experiance is more worthwile. Ie the more thats given to you that you could find on your own, the less accomplishment you have of your own.
This is ironic to find the occult, not sure of the symbols of the occult. After all, occult means "hidden," and hidden in both of the things we do and of the things that work behind what we do. I hope I don't ruin everyone's parade, so I will try to be universal. First of all, I don't know anything about the Triquetra--it has always been a mystery to me. It has a long history, and I have asked a real druid what it represents, even they are not totally sure, or not totally sure how it can be used, in magic. People generally think of the Pentagram as evil, but that is not so. It is said that christians actually used this symbol to ward off anything "evil." An example of this use would be putting the letters of the word, "SALVS," in the five chambers, which is latin for health. Letters separated, of course. Or, for people that speak and use English, it would be spelled "SALUS." The V is latin for U, in English. The pentagram is the five chambered, five lined symbol. It represents different elements of nature, and at the top is the divine spirit, but it doesn't show connection and harmony, just yet. Then there is the inverted pentagram, which has the opposite meaning to the "original" symbol. Satanists go by the inverted pentagram, which doesn't necessarily show harmony, but self-deification. The inverted pentagram is supposed to convey Satan, with the five chambers portraying himself. Then we go to the pentacle, which both the witch's and satanist's symbol both have: a circle making vertices. The pentacle, for the witches, represents a connection of all elements of nature and the divine spirit, into one. Then the Satanist's pentacle has Samael and Lilith, written inside the circle. Lilith is supposed to be Satan's wife. What the Witch's symbol and the Satanist's both have in common, when referring to the pentacle, is the notion of bonding. The circle at the vertices represents bonding.
I really don't know too much about the meaning behind the hexagram, but I know this. I know that the hexagram is actually comprised of two triangles, and they are interconnected. I actually do know the meaning, and it is this, "the symbol that symbolizes the connection between two worlds and the crossing of worlds: the spiritual, or other worlds, and the physical, or the world that normal people see." The hexagram when used in magic serves as a portal, which makes sense because to "hex" someone is to cast an "evil" spell, or black magic. This symbol, in my opinion has to be present, when casting a hex upon, or onto someone. Be careful using the word unto and onto, when pertaining to magic; it all has to do with karma. I asked the ouija board, one day, what the meaning behind the hexagram was, and it said a crossing between two worlds was correct.
What I just said, in abstract summarization, just as symbolism is brought out to be: The pentagram, when not inverted, represents the elements of nature, and the divine spirit. The pentagram, when inverted, represents someone or something above divine spirit(self-deification). The pentacles represent, because of the circle, a bonding. For the witch's pentacle it is all about harmony, with the environment. For Satanists, the pentacle is all about enlightenment and self-deification, and shows a bonding in Lilith and Satan as the King and the Queen of the underworld, and a bonding to make a person, more than just a person.
The pentacle, when not inverted, can be used for protection, and harmony in magic. The pentagram is a very powerful symbol. The pentacle, when inverted, can be used for one's own purposes and desires in magic.
The hexagram, is generally used for black magic, and represents the crossing of two worlds. So the symbol has to be present, for bad spirits to enter this world, when performing black magic. I am a Satanist, myself. I believe in and worship Satan and Lilith. I am very afraid of them. The beginning of all knowledge is to fear your deities, for this fear will instill the energy for spiritual change, in all things, and understanding. If you don't understand what i just said, try to understand a writer. A writer seeks knowledge, seeks experience, and seeks depth-perception to make sense of things, so that they can write awesome garbage. I hope this helped.
Symbolism carries abstract meanings with cool and interesting stories, along with them. I didn't get into any stories, but I got the meanings down. IN MY OPINION, SYMBOLS ARE THE DOOR WAYS TO AND FOR SPIRITUAL BEINGS, but the question is: is it about harmony or for one's own use.
You know, the problem with religion today is that people, in general claim that their religion is the right one. If the world had just one "religion," then I don't think the word, religion, would even exist. People wouldn't fight over what is right and what is not, when pertaining to a certain and "correct" "religion."