The Idea

Sankalpa(Sanskrit: संकल्प) means conception or idea or notion formed in the heart or mind, solemn vow or determination to perform, desire, definite intention, volition or will.This resolve or “Sankalpa” is universal to anyone embarking on accomplishing a goal however trivial or significant, because without the intention there is no action. It is not specific to just religious practices and rituals. It is a Universal concept.
In Sanatana Dharma, however, this practice of verbally uttering the Sankalpa mantra before engaging in a ritual, is prevalent.  Repeatedly stating one’s resolve to practice of higher thoughts and actions is believed to reinforce good values and guides our choices and consequently, the actions towards that goal.

A record of Why, When and Where

In practical terms, Sankalpa is also a kind of record of what you performed with finer details going down to the day and location of the ritual. It’s a diary of some sort.

Background

Before understanding the various parts of the Sankalpa mantra and what each denotes, perhaps it would be a good idea to get a quick recap of the cosmic cycle as it is described in various ancient texts, including the Bhagavata Purana. It’s mind-boggling.
In the Hindu Cosmic cycle,1 Mahayuga = Sum of 4 Yugas (Krita/Satya, Treta, Dwapara and Kali) = 4,320,000 years (of which the Yugas are divided in the ratio 4:3:2:1, Kali being the shortest)1000 such mahayugas comprise a day-time of Brahma (“The Creator”) also known as a Kalpa (“Aeon”).The kalpa is ruled by 14 Manus in succession.The reigning period of a Manu is one Manvantara which is 71.42 Mahayugas. There is an equivalent night-time of 4,320,000,000 years.The day-night of Brahma together constitutes one Brahma day (8.64 billion years).360 Brahma days constitute a Brahma year while 100 years represent the lifetime of Brahma which is the life of the cosmos.Doing this simple math gives the age of the cosmos as we know it now, to be 311 trillion years.
We are presently in the Sveta-Varaha kalpa in the reigning period of Vaivaswatha – the 7th manu. In this manvantara we are in the 28th mahayuga. As per our Cosmology, Brahma is supposed to have completed 50 Brahma years and is in his 51st year. That is why he is called “Parardha-dvaya-jivin” (i.e.) he lives for two parardhas. A parardha is half. Two halves make one. He is called so as he has completed one half of his tenure. These terminologies makes better sense in relation to the Sankalpa. 

The actual Sankalpa mantra

…. dviteeya parardhe – in the 2nd half of Brhama’s life  (Pratama= First, Dwitiya=Second)
Svetavaraha kalpe – in the kalpa of Sveta-Varaha (The Matsya, Vayu puranas give the names of the 28 kalpas)
Vaivaswatha manvantare – in the reigning period of the current manu (7th) – Vaivaswatha (The 14 Manus of the said Kalpa – Svayambhuva, Svarocisa, Uttama, Tamasa, Raivata, Chakshusha, Vaivasvata, Savarni, Daksa Sarvani, Brahma Sarvani, Dharma Sarvani, Rudra Sarvani, Deva Sarvani, Indra Sarvani)

Ashta Vimsati tame – in the 28th mahayuga of the current manavantara

Kaliyuge – in this kali yuga 
Prathame Padhe – in the first quarter of this yuga (Padha=Quarter, Pratama= First)
Jamboodveepe – this denotes the place where the ritual is performed.(Jambudveepa=India, being the center is surrounded by other Dveepas viz Plushka, Salmali, Kusa, Krouncha, Shaka, Pushkara) The Bhagavata purana describes these in detail, and interestingly these are the seven dveepas/continents separated by seven types of oceans.
Bharata Varshe, Bharata Kande – in the land of Bharat
Sakhabde Mero, Dakshine Parsve – to the South of the Meru mountain
Asmin Varthamane Vyavaharike – in the current period now reigning
Prabhavadi Shasti Samvatsaranam Madya – among the cycle of 60 years starting from Prabhava
….Nama Samvatsare – the name of the year in the 60 year cyclic Hindu calendar
….Ayane – Dakshinayane (July – Jan) or Uttarayane (Jan – July)Uttarayana is the northward movement of the Sun on the celestial sphere. The six month period between winter and summer solstices. The complement of Uttarayana is Dakshinayana , when the Sun travels southward on the celestial sphere.….Ritou – denotes the 6 seasons or Ritus – (Vasantha, Greeshma, Varsha, Sharadh, Hemantha and Shishira denoting Spring, Summer, Monsoon, Autumn, pre-Winter and Winter seasons)
….Maase – one of the 12 lunar months (Mesha, Vrishaba, Mithuna, Kataka, Simha, Kanya,Thula, Vrischika, Dhanur, Makara, Kumba, Meena)
….Pakshe – (Sanskrit: पक्ष) refers to a fortnight in a month of the lunar calendar.Shukla Paksham(Shukla = White/bright) is the period starting the day after Amavasya/New Moon,  until and including Pournami/Full Moon , denoting the period of the waxing moon. Krishna Paksham (Krishna = dark) is the period starting the day after Pournami until and including Amavasya, denoting the period of the waning moon.
….Subha Thithou – one of the 15 days between Pournami and Amavasya (Prathama, Dvithiya, Trithiya, Chaturthi, Panchami, Shasti, Saptami, Ashtami, Navami, Dasami, Ekadasi, Dwadashi, Trayodasi, Chaturdasi, Pournami/Amavasya)
….Vasara Yuktayam – one of the days of the week (Bhanu, Soma, Bhowma, Soumya, Guru, Brugu and Sthira, denoting Sunday through Saturday)
….Nakshatra Yuktayam – the day’s star or Nakshatram ( In the lunar calendar, there are 28 stars that rise and set on the ecliptic of the celestial sphere through the month and this cycle repeats every month)
….and then proceed to state the intention or the resolve.
It is quite an interesting exercise in these modern days to stop and reflect on the timelines that the Sankalpa mantra describes. More than being a mere documentation of the time and place, it reminds us of the insignificance of one’s lifespan in the BIG picture. And that, is often necessary for us to stop and reflect on our purpose of life and elevate our thoughts to higher ideals. That is the power of Sankalpa.