I wish to know everything about these two terms. If these are related to destroying everything except yourself then what good I should learn from these terms, instead of getting afraid of these?
Tandava is the divine dance performed by Lord Shiva. In Shaiva Siddhanta tradition, Lord Shiva in the form of 'Nataraja' is considered the supreme lord of dance. The Tandava takes its name from 'Tandu', the attendant of Lord Shiva, who instructed Bharata (author of the Natya Shastra) in the use of Angaharas and Karanas, modes of the Tandava at Shiva's order.
According to wiki article:
The 32 Angaharas and 108 Karanas are discussed by Bharata in the 4th chapter of the Natya Shastra, Tandava Lakshanam. Karana is the combination of hand gestures with feet to form a dance posture. Angahara is composed of seven or more Karanas. 108 karanas included in Tandava could be employed in the course of dance, fight, and personal combats and in other special movements like strolling.
The dance is a pictorial allegory of the five principal manifestations of eternal energy:
'Srishti' (सृष्टि) - creation, evolution
'Sthiti' (स्थिति) - preservation, support
'Samhara' (संहार) - destruction, evolution
'Tirobhava' (तिरोभाव) - illusion
'Anugraha' (अनुग्रह) - release, emancipation, grace
Thus Tandava symbolizes the cosmic cycles of creation and destruction, as well as the daily rhythm of birth and death.
Tandava is not always the voilent one. There are mainly 2 types of Tandavas, ie, Ananda Tandava and Rudra Tandava. However, in some sources there are 7 to 16 types of Tandavas. While Rudra Tandav is the voilent one which causes destruction, Ananda Tandava on the other hand is the non-voilent one, which Lord Shiva performs out of his joy. Ananda Tandava is sometimes practised by Him along with Goddess Parvati. Goddess Parvati's dance form is called Lasya which she performs in response to Lord Shiva's Tandava.
Also, Tandava is not only practised by Lord Shiva only. There are other Gods and Goddesses also performing Tandava, e.g., Goddess Kali, Lord Ganesha, Lord Krishna, Indra, etc.
Source: Wiki Article
Shiva Tandava has nothing to do with destruction but rather with creation. Here is an interpretation in terms of the 'dance of the consciousness':
The whole creation is the dance of one consciousness (Shiva). The one consciousness danced and manifested into a million species in the world. So this infinite creation is the dance of Lord Shiva or Shiva Tandav.
The whole world is a place of Shiva.
Excerpts from a talk by Sri Sri Ravi Shankar: https://xa.yimg.com/kq/groups/17184919/.../understandingshiva.pdf