Mantra is associated with speech, speech is associated with "wind," wind is associated with mind. This is a condensed summary, as one way to answer the question, "Why use mantras?"
The PrajnaparamitahridayaSutra is said to have an even shorter version....
Mantras are also said to be the condensed meaning of tantras...in this case, the mantra is in a sutra. (This, to me, is an interesting question--how does a well-known sutra have a mantra associated with it? But that's a tangent....)
I think the meaning of this mantra does condense the sutra--it can be translated. It can be a mnemonic device, and a tool for contemplation of the meaning of the sutra.
Also, although I become a bit "uncomfortable" with the idea of "magic" and mantras, I have to admit that it's an easy association to make, especially if one actually reads the tantras and takes them at face value--ChakrasamvaraTantra and HevajraTantra, just as two examples, do include instructions for rituals utilizing mantra for various purposes, and, taken literally, they are similar to "magical rituals" as we might understand them in the West. In particular, the rituals regarding the "Four Activities"--pacifying, magnetizing, enriching, and destroying--could be seen this way.
"Absolute Truth is not an object of analytical discourse or great discriminating wisdom,
It is realized through the blessing grace of the Guru and fortunate Karmic potential.
Like this, mistaken ideas of discriminating wisdom are clarified."
- (Kyabje Bokar Rinpoche, from his summary of "The Ocean of Definitive Meaning")