A hybrid or cross-breeding is a result of sexual reproduction between two different types of plants or animals. So they produce the hybrid of two recognizable parents.
Known (and not reproductive) hybrids of animals are e.g. liger / tigon, mule / hinny, sheep-goat, a cross between a camel and a dromedary.

In plant breeding, the first generation after a cross is called an F1 hybrid, the second generation an F2 hybrid, etc. Many cultivars are F1 hybrids between two inbred lines. This gives a great achieved uniformity. (The "F" stands for filius, the Latin word for son.)
A hybrid combines of two parent plants the desired properties. Their seed (if they are fertile) ensure that however absolutely not.
A hybrid is a uniform crop regarding shape, color, yield and other characteristics. In monoculture it is important to harvest equal quality and at the same time.

For animals, the same applies.

Plant names with an "X" are always crosses between two species of the same Genus, either or not spontaneously. Only very closely related plants can be crossed. Mother Nature is unpredictable. The above rules give only a general frame of reality. And on almost every rule there are exceptions again.
Hybrid species are generally not fruitful because the chromosome pairs differ too much from each other. But on a doubling of the number of chromosomes there are sometimes exceptionally prolific species.

You can yourself as a gardener grow and exchange seeds. www.bingenheimersaatgut.de. is a cooperative with more than 100 growers. (Germany, Netherlands, France, Italy). They operate under their own management to raw material suitable for organic gardening.
Info can be found on http://www.zelfzadentelen.be/ (with the support of the Flemish Government and the European Agricultural Fund, not yet Monsantood).