Here is a simple explanation of each of the 32 names of Durga and their significance:

1. दुर्गा (Durga): The one who removes obstacles and difficulties.

2. दुर्गातिशमनी (Durgaatishamani): The one who ends extreme suffering and difficulties.

3. दुर्गापद्धिनिवारिणी (Durgapaddhininivaarini): The one who removes obstacles on the path of righteousness.

4. दुर्गमच्छेदनी (Durgamachchedani): The one who cuts through all difficult situations.

5. दुर्गसाधिनी (Durgasaadhini): The one who helps achieve success even in tough situations.

6. दुर्गनाशिनी (Durganaashini): The one who destroys all hardships.

7. दुर्गतोद्धारिणी (Durgaatoddhaarini): The one who lifts up those who are in trouble.

8. दुर्गनिहन्त्री (Durganihantri): The one who destroys the sources of difficulties.

9. दुर्गमापहा (Durgamaapahaa): The one who removes difficult obstacles.

10. दुर्गमज्ञानदा (Durgamajnaandaa): The one who provides wisdom to overcome difficulties.

11. दुर्गदैत्यलोकदवानला (Durgadaityalokadavaanalaa): The one who is like fire for evil forces, burning them away.

12. दुर्गमा (Durgamaa): The one who is difficult to reach without true devotion.

13. दुर्गमालोका (Durgamaalokaa): The one who has a divine, difficult-to-attain vision.

14. दुर्गमात्मस्वरूपिणी (Durgamaatmaswaroopini): The one who represents the true self that is difficult to realize.

15. दुर्गमार्गप्रदा (Durgamaargapradaa): The one who shows the path through difficulties.

16. दुर्गमविद्या (Durgamavidyaa): The one who possesses deep, sacred knowledge.

17. दुर्गमाश्रिता (Durgamaashritaa): The one who shelters those facing difficulties.

18. दुर्गमज्ञानसंस्थाना (Durgamajnaanasansthaanaa): The one who is the source of knowledge to overcome difficulties.

19. दुर्गमध्यानभासिनी (Durgamadhyaanabhaasini): The one who shines in meditation, leading out of difficulties.

20. दुर्गमोहा (Durgamohaa): The one who removes delusions and confusion.

21. दुर्गमगा (Durgamagaa): The one who shows the right way out of difficulties.

22. दुर्गमार्थस्वरूपिणी (Durgamaarthaswaroopini): The one who represents the ultimate goal of overcoming difficulties.

23. दुर्गमासुरसंहन्त्रि (Durgamaasurasanhantri): The one who defeats evil forces.

24. दुर्गमायुधधारिणी (Durgamaayudhadhhaarini): The one who holds weapons to overcome challenges.

25. दुर्गमांगी (Durgamaangi): The one who has a powerful form that is hard to understand.

26. दुर्गमता (Durgamataa): The one who is beyond all difficulties.

27. दुर्गम्या (Durgamyaa): The one who is difficult to reach without true dedication.

28. दुर्गमेश्वरी (Durgameshwari): The supreme goddess who rules over all difficulties.

29. दुर्गभीमा (Durgabheema): The one who is terrifying to those who create difficulties.

30. दुर्गभामा (Durgabhaamaa): The one who is beautiful and protects her devotees.

31. दुर्गभा (Durgabhaa): The one who is radiant and brightens the path for her devotees.

32. दुर्गदारिणी (Durgadaarini): The one who removes all obstacles and dangers.

These names highlight different aspects of Durga, showcasing her as a powerful force who helps her devotees overcome all difficulties, challenges, and evil forces.