Tantra in its original meaning is a very wide-spread definition and includes quite a wide variety of different practical, mystical and philosophical schools of thoughts.
Originally, the Agama Sastra, this means the compendium of scriptures regarding Tantra, was revealed by Lord Siva to his Goddess Sakti. Agama therefor means a secret teaching from God in form of Siva to Goddess in form of Sakti, and the content of those scriptures was mostly of practical approach.
But as with so many belief "systems", Tantra has gone through an evolution in itself regarding its fundamental and essential teachings.
The summit of Tantric knowledge was reached in the region of Kashmir from around 900 AD to 1200 AD. It was at this time, that the various Agama Shastras mentioned above, which were "contradictive" towards eachother in the sense that some taught pluraslism / polytheism, some monism, some were purely occult, etc. came to be joined together and were turned into a highly-interesting, philosophical and yet mystical Tantric system called "Trika Shaivism", also called "Shavisim of Kashmir" eventhough latter expression is not really appropriate since the system isn't bound specifically to the region of Kashmir.
Tantra in historic and systematized sense can be split up in 4 sects or schools of thought, this is Krama, Kula, Spanda and Pratyabhijna (in order of historic appearance).
The first two are oriented towards worshipping God in his female aspect viz. in his power aspect and are more esoteric and cult-like in their nature (eventhough all Tantric systems share some esoteric fundamentals), also called Saktism since it is the Sakti-aspect that is the main focuss of those 2 schools. Spanda is also about the power-aspect of God, eventhough the Spanda Yogi more focusses on his awareness of existence and certain moments within the act of perception in which the totality of one's own nature, viz. Shiva as pure, universal consciousness, can be experienced. Pratyabhijna is the philosophical, abstract doctrine, in which the philosophical extracts from the different Agama Shastras, are put together to a highly mystical, philosophical, yet practical theology of awareness. Such are the four main schools, that had been developped throughout the 3rd AD up to the 12th AD. Eventhough those are four "schools" as such, they are in their doctrine, their teaching, and their practical aspects interwoven and cannot clearly be seperated. "Trika Shaivism" as such is the summit in the sense that it combines the fundamentals of all those 4 schools and turns them into one non-dual system of thought and of mystical practice. Great philosophers and yogins such as Uptaleva, Abhinavagupta or Kshemaraja brought the system to a level of mystical insight which, in my eyes, can hardly be compared to any other mystical school of thought.
As at the time of the foundation of Trika in Kashmir, Kashmir was also an important place for Buddhists and Vedantists, the Trika Shaivism is also influenced by Buddhist and Vedantic thought and therefor is like a complex combination of all the important systems at that time, without losing its original foundation which is laid in the Agama Shastras viz. the Tantric scriptures.
As regards the philosophy behind Tantra, Tantra is a non-dual philosophy, meaning that God or Reality is one. While Vedanta claims Brahman to be a passive, divine reality on which our universe is superimposed on and therefor is "less than real" (viz. the universe), the Tantric considers the universe to be a real expression of God, and hence God as the "dancing Shiva" is in constant action, constant movement, experiencing consciously every coginition he is aware of within himself, through himself. He as universal, absolutely free consciousness is therefor the true essence of all being, and through his goddess Shakti, viz. his power which is self-awareness, he is able to emanate the universe through himself within himself and reflect on himself. The universe is therefor a reflection within God, and yet it is not illusory in nature. It is the way God expresses himself, is aware of himself and experiences/perceives himself.
Hence in order for that universal consciousness to manifest itself in itself, in needs to contract viz. limit itself into mental and material shapes. Only in this way God can actually manifest himself. The individual is therefor a contracted form of God-consciousness viz. Siva and the cause of this is the ignorance the individual has about his real nature.
Consciousness in terms of God's universal consciousness has therefor 2 aspects: the inner aspect of an undivided awareness, an "all-in-one-unity"-awareness it has of its own, and an outer aspect, where it manifests itself, and by manifesting itself, its undivided awareness gets divided through the different cognitions through which it recognizes itself.
Hence God in his static, transcendental Siva-aspect is the pure, all-pervasive light of undivided and universal consciousness, while in his immanent, dynamic Sakti-aspect, he is self-awareness or "power" in the sense that through being aware of himself and therefor recognizing and reflecting on himself, the universe is emanated viz. manifested in himself by his reflection.
I could write for hours and yet not be able to describe the processes of manifestation and self-awareness in all their detail as well as all the other apsects of this doctrine, so I recommend you to go find some information about it in books or on the web.
Considering the "westernized" Neo-Tantra of today, or the watered-down forms of Tantra in the west, I want to emphasize the clear difference between the original thought of Tantra in India, and the "neo-Tantra" hocus-pocus which is now available in the West.
If you clearly want to explore the nature of Tantra, you should focuss your attention on the original scriptures and philosophers.