In Shiva Sutra, it is mentioned that the Kalaa are divided into 5 types Nivrtti, Pratishtha, Vidya, Shanti , Santyatita . Each Kalaa has set of Bhuvanas, for example Pratishtha Kalaa has 56 Bhuvanas, Vidya Kalaa has 28 bhuvanas.
So my question is, what are these Bhuvanas ? What is significance of Bhuvanas with respect to Kalaa ?
Most of the info is already given in this answer.
Bhuvanas are planes of existences which exist both in the outer world as well as inside the aspirant's body. As the aspirant progresses spiritually he experiences within himself these Bhuvanas existences.
First, note that Kala is one the 36 Tatvas of Shaktism (as well as Shaivism).
In Shaktism, as well as in Shaivism, there are 36 Tattvas. Shiva/Shakti, Vidya, Maya, Purusha, Prakriti, Iswara, etc to the Panchabhutas are these 36 Tattvas.
These Tattvas are again grouped into Shuddha (pure), Shuddhashuddha (mixed) and Ashuddha (impure) categories.
Now, certain Bhuvanas (or worlds) are assigned to several of these Tattvas. That is, the Tattvas own certain Bhuvanas. The Tattvas also have respective Kalas (kalA i.e part) associated with them.
The complete list of all the Bhuvanas owned by these Tattvas are as follows:
Shiva Tattva's Bhuvanas (10 in number) - Anashrita, Anatha, Ananta, Vyomrupini, Vyapini, Urdhagamini, Mochika, Rotika, Dipika and Indhika.
Shakti Tattva's Bhuvanas (5) - Shantyatita, Shanti, Vidya, Pratishtha and Nivritti. (Vaindavpura is the alternate name for these Bhuvanas)
Sadashiva Tattva's Bhuvanas (1) - Sadashiva Bhuvana.
Iswara Tattva's Bhuvanas (8) - Shikhandi, Shrikantha, Trimurti, Ekanetra, Ekarudra, Shivottama, Sukshma and Ananta.
Suddhavidya Tattva's Bhuvanas (9) - Manonmani, Sarvabhutadamani, Balapramathini, Balavikarini, Kalavikarini, Kali, Raudri, Jyeshtha and Vama.
Maya (8) - Angushtamatra, Ishana, Ekekshana, Ekapingala, Udbhava, Bhava, Vamadeva, and Mahadyuti.
Kala (this is KAla) Tattva's (2) - Shikesh and Ekavira.
KalA Tattva (this is KalA) (2) - Panchantaka and Shura.
Vidya Tattva (2) - Pinga and Jyoti.
Niyati Tattva (2) - Samvarta and Krodha.
Raga Tattva (5) - Ekashiva, Ananta, Aja, Umapati and Prachanda.
Purusha Tattva (6) - Ekavira, Ishana, Bhava, Isha, Ugra, Bhima and Vam.
Prakriti Tattva (8) - Shrikantha, Aum, Kaumara, Vaishnava, Brahma, Bhairava. Krita and Akrita.
Buddhi Tattva (8) - Brahma, Prajesh, Saumya, Aindra, Gandharva, Yaksha, Rakshasha and Pishacha.
Ahamkara Tattva (1) - Sthuleswara
Bhuvanas owned by Manas (mind) and Pancha Gyana Indriyas (1) - Sthuleswara.
Pancha Karma Indriyas (1) - Shankukarna
Pancha Tanmatra's (5) - Kalanjara, Mandaleswara, Makota, Dravinda and Chakalanda.
Akasha Tattva (8) - Sthanu, Swarnaksha, Bhadrakarna, Gokarna, Mahalaya, Avimukta, Rudrakoti and Vastrapada.
Vayu Tattva (8) - Bhimeswara, Mahendra, Attahasa, Vimalesh, Nala, Nakala, Kurukshetra and Gaya.
Teja Tattva (8) - Bhairava, Kedara, Mahakala, Madhyadesha, Amratak, Jalpesh, Shrishaila, Harishchandra.
Apa Tattva (8) - Lakulisha, Parabhurti Dindi, Mundi, Vidhi, Pushkara, Naimisha, Prabhash and Amaresha.
Prithvi Tattva - Highest no of Bhuvanas are assigned to it - around 108.
In the Rig Veda 10.10.125.7 the Goddess says through Rishika Vak:
aham suve pitaramasya murdhan mama yonirpasvantah samudre |
Tato vitishte bhuvanAnu viswo tAmum dyAm varshanopa sprishAmi ||
The 2nd line's meaning is:
Therefore, I exist in all of these Worlds (Bhuvana), in various forms
The Goddess is known by the name of Bhuvaneswari because she is the supreme controller of all these Bhuvanas (whether internal or external).
The Kubjika Tantram specifically says that:
BhuvanAnAm pAlanatvAd bhuvaneshi prakirtitA |
Srishti stithi kari devi bhuvaneshi prakirtitA ||Since She maintains (or rules) all these Bhuvanas, the Goddess, who creates, maintains and destroys, is known by the name of Bhuvaneswari (or Bhuvaneshi).
PrAnatoshini Tantra, KAnda 5, Parihcheda 6
Bhuvaneswari = Iswari (supreme controller) of the Bhuvanas (worlds).
Bhuvana's another meaning is "asmAt bhavati iti bhuvanam" or "Loka" or "place of birth/creation".
Parama-Shiva or Brahma is both Nirguna and Saguna. Parama-Shiva, when Saguna, is called 'Sakala' ie coupled with Shakti or Aadi-Prakriti or Chit-Shakti (Who is the source of all kalaas).This Sakala-Shiva is the source of all creation represented by Sabda and Artha. This creation consists of sixtythree tattwas. Shabda or word and its artha or meaning are always coupled together. Shabda is Vachaka and Artha is Vachya. There are two types of meanings: Sthula or Gross and Sukshma or Subtle. Artha is created by Kalaa, Tattwa and Bhuvana.
Kalaas are forms of the Adi-Prakriti or Chit-Shakti. According to Satthimsatattwa, there are five principal forms of Kalaa : Nivritti, Pravittri, Vidya, Shanti and Shantyatita.
Kshititattwa arises from Nivitrikala (also known as the Kulakundalini Shakti), Aptattwa from Pratisthakala, Tejastattwa from Vidyakala, Maruttattwa from Shantikala and Vyomatattwa from shantyatitakala.
The word Bhuvana means 'bhavati asmat' (arises from this). Bhuvanas are costructed by the sixtythree tattwas.These are different planes of Praana and Bodha of a sadhaka.
Santyatitakala has two tattwas(Shiva, Shakti) and 15 bhuvanas. Shantikalaa has three tattwas (Sadashiva, Ishwara, Suddhavidya) and 18 bhuvanas. Vidyakalaa has twentysix tattwas (Maya, Kaala, Kalaa, Vidya, Niyati, Raaga,Purusha,Prakriti,Buddhi, Ahamkaara,Manas, 5 Karmendriyas, five jnanendriyas, Five tanmaatras,Vyomatattwa,Maruttattwa,Tejastattwa,Aptattwa) and 83 bhuvanas. Nivrititattwa has Kshititattwa and 8 bhuvanas.
Reference: Saastramulak Bharatiya Shaktisadhana, Upendrakumar Das,RMIC, Vol. 1, chapter 10. Names and details of all the Kalaas and Bhubanas are given there. I could provide scanned copies (bengali) if required.