For this you will have to use view module.
Step 1: Create a new view from Administration > Structure > View. Click on + Add new view.
Step 2: Give a name to your new view. From 'Show' select Taxonomy terms and from type select appropriate taxonomy vocabulary (I assume name is 'product' here). Check either page or block and click 'Continue & edit'.
Step 3: In First Page or Block under 'Filter Criteria' click on Add and select Taxonomy Vocabulary and set it to use product. Click on Add again from Filter Criteria and select Taxonomy term and set it to Parent term 1, Parent term 2, ..... Now in preview section you will see the Parent terms.
Step 4: Under FIELDS click on Add and select Taxonomy term: Term ID and click on Apply. In Configure field page check on Exclude from display and click on apply. (I assume Taxonomy term: Name is already there.)
Step 5: Rearrange the order of fields by clicking on drop down icon besides Add under FIELDS. Make user the Term ID appears above Term Name and Apply.
Step 6: Click on Taxonomy term: Term Name and expand REWRITE RESULTS. Click the checkbox Rewrite the output of this field and in text area name Text, type in [name] and Apply.
Step 7: Create a new page in same view +Add > Page or create a different view as in Step 1 & 2.
Step 8: In new view page set the path under PAGE SETTINGS to subchild/tid (here tid refers to parent tid or taxonomy id).
Step 9: Follow the steps 3 to 6. Instead of Parent term 1, select Child term 1.1, Child term 1.2, ... assuming Parent is 1. And set href to child/tid for step 6 here tid refers to child term 1.* tid.
Step 10: Follow the same procedure as in step 8 & 9 for other child terms.
Step 11: Follow the same procedure as in Step 8 to 10. However set path under Page Settings to subchild/tid and href attribute for step 6 would be product/tid, here tid is subchild tid or taxonomy ID.
Step 12: Follow the same procedure as in Step 11 for all subchild terms.
For Displaying Products:
Step 1: Create a new View from Administration > Structure > View. Click on + Add new view.
Step 2: Select Content from Show with appropriate type. Check on page and click on Continue & edit.
Step 3: Set the path in Page Settings to product/tid and from Filter Criteria select the Taxonomy term appropriate to the product to be displayed.