"Durga Chalisa" is a prayer addressed to Goddess Durga, the Supreme Mother of all beings. A 'Chalisa' is a rendition that contains 40 stanzas/verses.
It is a rendition by a saint named Devidas. The last verse (41st stanza) confirms this fact. But I don't know much about him. A saint named Devadas of Gujarat lived in the 18th century. However, these verses are in Awadhi. So, it could be a different saint.
I’ve combined both lines of the verse into one, marking the break in the middle to keep the post compact.
The meanings of the verses are provided at the bottom of the post so you can recite the prayer continuously.
Durga Chalisa
nirAkAr hai jyOti tumhAri | tihoo lOk phaili ujiyAri || (2)
sashi lalaat, mukh mahA vishAlaa | nEtra laal bhrukiti vikarALaa || (3)
roop maatu kO adhika suhAva | daras karat jana ati sukh pAvE || (4)
tum sansAr shakti laya keenA | pAlan hEtu anna dhana deenA || (5)
annapoorNa hui jag paalaa | tum hee aadi sundari baalA || (6)
pralay-kaal sab nAshan haari | tum Gouri Shiv-Shankar pyaari || (7)
Shiva yOgi tumharE guN gaavE | Brahma Vishnu tumhe nit dhyAvE || (8)
roop Saraswati kO tum dhArA | dE subuddhi rishi-munin ubArA || (9)
dharyO roop Narsimha kO ambA | pragat bhayee phaadkar khambA || (10)
rakshA kar Prahlad bachAyO | HiraNyakashipu ko svarg pathAyO || (11)
Lakshmi roop dharO jag maahi | Shri Narayan anga samAhee || (12)
ksheer-sindhu me karata vilaasa | dayAsindhu deejai manu aasa || (13)
HingalAj mE tumhi Bhavani | mahimaa amit na jaat bakhaani || (14)
MAtangi aur dhoomAvati mAtA | BhuvanEshwari bagalaa sukh dAtA || (15)
Shri Bhairav, TArA, jagatAriNi | cchinna bhaal, bhava dukha nivArinee || (16)
KEhari vaahan sOha Bhavani | laangur veer chalat agavaanee || (17)
kar mE khappar-khadg virAjai | jAkO dEkh kaal dar bhAjai || (18)
sOhai astra aur trishoolA | jAtE uthat shatru hiya shoolA || (19)
nagara kOti mE tumahi virAjat | tihu lOk mE dankaa baajat || (20)
shumbha nishumbh daanav tum mArE | Raktabeej Shankhan samhArE || (21)
MahishAsur nrup ati abhimAnee | jEhi agha bhAr mahee akulAnee || (22)
roop karaal KALi-kaa dhArA | sEna sahitu tum tihi samhArA || (23)
paree gaadh santanu par jab jab | bhaee sahaay maatu tum tab tab || (24)
amarapuri aru baasav lOkA | tava mahimA sab rahE asOkA || (25)
jwAlA mE hai jyOti tumhAree | tumhE sadaa poojE nar-naaree || (26)
prEm bhakti sE jO yah (yash) gAvai | dukha daridra nikat nahi Avai || (27)
dhyAvE tumhE jO nar mana laayee | janma-maraNa taakou chuti jaayee || (28)
jOgee sur muni kahata pukAree | yOg na hO bina shakti tumhAree || (29)
Shankar Achaaraj tapa keenhO | kaama krOdha jeet sab leenhO || (30)
nishidin dhyan dharo Shankar kO | kaahu kaala nahi sumirO tumakO || (31)
shakti roop ka maram na pAyO | shakti gayee tab manu pachitAyO || (32)
sharaNAgat hui keerti bakhAnee | jai jai jaya Jagadamb BhavAnee || (33)
bhayee prasanna aadi Jagadamba | dayee shakti nahi keen vilambA || (34)
mOkO matu kasht ati ghErO | tuma binu kaun harE dukh mErO || (35)
aashA trushNa nipatu satAven | mOha madAdika sabu vinAshaven || (36)
shatru nAsha keejai maharaaNee | sumirou ikachita tumhE Bhavani || (37)
karO krupA hE mAtu dayAlA | riddhi-siddhi dE karahu nihAlA || (38)
jab lagi jiyavu dayaa-phal paavoo | tumharO yash mai sadaa sunAvoo || (39)
Durga chAlisaa jO nit gaave | sab sukh bhOgu paramapad paave || (40)
Devidas sharaN nija jaani | karahu krupA Jagadamba Bhavani ||
Durga Chalisa Meanings (in English)
(1) I offer my salutations to you, O Goddess Durga, the Giver of Joys. I bow to Thee, O Mother Amba, the Remover of Sorrows.
(2) You are the Formless and all-pervading Glowing Light that encompasses all the Three Worlds.
(3) Your forehead is the Moon, and your face is much larger. Your eyes are red and frightening, filled with a stern frown.
(4) O Mother, your form is enchanting, the sight of which provides immense joy.
(5) The entire life of the worlds is in your abode; you are the provider of food and prosperity for their survival.
(6) You became Annapurna to nurture the whole universe; you are the timeless Sundari Bala (Balatripura Sundari).
(7) At the time of Dissolution, you are the Destroyer of the worlds. You are the beloved consort Gauri of Shiva-Shankara.
(8) Lord Shiva and the yogis chant your praises; Brahma and Vishnu meditate on you.
(9) It is you who took the form of Saraswati and provided wisdom to the sages and yogis.
(10) O Mother, you took the form of Narasimha and appeared, tearing out the pillar.
(11) To protect Prahlad and send Hiranyakashipu back to heaven (Hiranyakashipu was the gatekeeper of Vishnu Loka who was cursed to be born as a demon).
(12) Assuming the form of Lakshmi, O Mother, you reside inside Shri Narayan.
(13) Dwelling with joy in the Ocean of Milk, O Benevolent Mother, fulfil my wishes.
(14) O Mother Bhavani, you are the Goddess in the Hingalaja temple. Your glories are innumerable and beyond description.
(15) You are Maatangi and Dhoomavati. You are Bhuvaneshwari and Bagalamukhi; bring us happiness.
(16) O Mother, it is you who, to redeem the world, appeared in the forms of Shri Bharavi, Tara, and Chhinnamasta Devi (severing your own head), to end the sorrows of the world.
(17) Riding on your Lion, O Bhavani, the long-tailed brave monkey (Hanuman) leads in front.
(18) Holding a skull (skull-cup) and sword in your hands, your form is frightening and shivers even the time.
(19) Armed with the Trident in your hand, you make the enemy's heart pound with the stings of fear.
(20) You are the Goddess Vajreshwari residing in the Nagarkot temple (Himachal Pradesh), and your glory echoes across the three worlds.
(21) You slayed the demons Shumbh and Nishumbha, and many other demonic forms like Raktabeeja, Shankhan, etc.
(22) When the proud and arrogant demon king Mahishasura's evil deeds spread throughout the world and distressed Mother Earth...
(23) You assumed the frightening form of Kalika Devi and killed that Buffalo Demon along with his entire army.
(24) Whenever the saints got troubled, it was you who kept rescuing them.
(25) All the abodes, including Amarapuri (Heaven) and Basavalok (abode of Shiva Ganas), are griefless because of your grace.
(26) It is the glow of your glorious virtues that is burning in the Shri Jwala Temple (Kangra, Himachal Pradesh), where all men and women worship you.
(27) Whoever sings (your) such glories with pure love and devotion, grief and sorrows do not reach them.
(28) He who concentrates on you with meditation traverses the cycle of births and deaths.
(29) All yogis, angels, and sages loudly declare that without your power and grace, they cannot establish union with God.
(30) Param Guru, Adi Shankaracharya, had performed great penance and established control over all desires and anger.
(31) He meditated day and night on Lord Shankar, but never thought of you even for a while.
(32) Since he did not recognise your Shakti form, his entire powers vanished, and then he repented of his mistake.
(33) Then, he sought your refuge and got fame, and sang your glorious deeds, chanting "victory, victory, victory, to thee, O Mother of Worlds, Bhavani".
(34) Mother Durga became pleased with him and immediately bestowed all the lost powers and fame.
(35) O Mother, I am entangled in many pains and grief. Other than you, who is there to ease my worries?
(36) Desires and greed are tormenting me. Lust and arrogance are destroying me.
(37) O Goddess, please destroy these enemies. I will meditate upon you with full concentration (O Bhavani!).
(38) O Mother Benevolent, please show grace. Provide me with material prosperity and spiritual wealth.
(39) While I am alive, I keep singing your glories while meditating upon you.
(40) Whoever recites this Durga Chalisa daily, he will attain the eternal abode of moksha.
Ending Sloka Meaning:
Treating Devidas as your beloved being, O Mother Bhavani, bestow your grace upon me.

