What is Hinduism is a pretty open ended question to be fair. How was I supposed to know which element of Hinduism you wanted an answer about? My perception of Hinduism being tied to the Indian race might well be wrong, if it is you can correct me, I am here to learn.
Hinduism is basically an amalgamation of hundreds of indic beliefs and practices that originated over a period of time.
It's just impossible to define it properly as there are no common set of rules or regulations . It initially began as the religion of Vedic Aryans but later on acquired and subsumed various other philosophies and practices .
If we get down to the basics , there are 6 prime philosophies in Hinduism.
1. Samkhya - According to it the presence of divine agency is not essential to the creation of world. The world owes it's creation and existence more to the nature or Prakriti than God. This was a rational and scientific view.
2. Yoga - According to this , a person can attain salvation through meditation and physical application. Practice of control over pleasure and senses is central to this system.
3. Nyaya - According to it , salvation could be attained through acquisition of knowledge.
4. Vaisheshika - This one gave importance to discussion of material elements. BTW this school propounded the atom theory believing that all material objects are made up of atoms.
5. Mimansa - As per this , the Vedas contain the eternal truth and the principal objective of this philosophy was to acquire heaven and Salvation. A person will enjoy the bliss of heaven so long as his accumulated acts of virtues last. When they are exhausted , he will return to earth , but if he attains salvation he will be completely free from the cycle of death and birth.
MOST HINDUS BELIEVE IN THIS SCHOOL although they don't know it.
6. Vedanta - This one is my favorite. It literally means the end of the Veda. As per this , The Brahma or God is Nirakar (that is Without any form) and Nirguna( Without any attributes) . It lays stress on attaining knowledge to fulfill the objective of salvation. This philosophy could be traced to earlier Upanishads.
Basically , Brahma is the reality and everything else is Maya (unreal) . The self (soul) coincides with Brahma. Therefore if a person acquires the knowledge of self, he acquires the knowledge or Brahma and thus attains salvation.Both Brahma and Soul are eternal and indestructible.
The theory of karma came to be linked to this Philosophy.