As you may have noticed that these mantras are quite different from Vedic mantras or those contained in other Hindu Shastras although they are also (mostly)related to Vedic Deities only.
They use mostly spoken languages as opposed to sanskrit and also at times the words used in them are such that the mantras look completely meaningless.
For example, given below is one such mantra dedicated to Goddess Saraswati(which is supposedly for removal of negative energy,but don't just chant this of course):
Sarasvatī gāḍī sunna kā dīyā rupē kī bātī guṇa bātī bātī. Aṅkīnī,
ḍaṅkīnī, śaṅkhinī, jādū ṭōnā mērī bhavānī isī ghaḍī yahām̐ sē nikala
jāya, mērī a̔āna mērē gurū kī a̔āna īśvara gaurā pārvatī mahādēva kī
But they do make good use of the Pranava(Om) .
For example,the following is a mantra for the Natha sampradaya Guru Gorakshnath:
Satya Naam AAdesh Guru Ka Om Guru Gorokhnathaya Namaha
And,following is a shabar mantra for Goddess Durga:
Om Ath Bhuji Ambika Ek Naam Omkar Khat Darshan Tribhuvan Mein Panch
Pandava Saat Deep Chaar Khoont Nau Khand Mein Chnada Suraj Do Praman
Haath Jodh Binti Karoon Mam Karoo Kalyan.
They are related to the Natha Sampradaya.
The propounder of such mantras are the Natha Sampradaya Gurus like Gorakshnath,Matsyendranath etc.
All of them are descendants of the first Guru or Adi Natha or Lord Shiva.
The famous Yoga treatise "Hatha Yoga Pradipika" lists few Siddha Gurus of this Parampara among whom one is called Shabar.
I assume that the mantras are named after him.
Sri Âdinâtha (Śiva), matsyendra, Nâtha, Sâbar, Anand, Bhairava,
Chaurangi, mîna nâtha, Goraksanâtha, Virupâksa, Bileśaya.
According to some web pages these mantras are auto-energized or siddha but some others claim that a regular diksha(initiation) is needed from a proper Guru before chanting them.
It is also believed that these mantras are more effective in Kali Yuga than any other mantras.