Page displaying posts from specific categories

I’ve done this in the past, I just can’t remember for the life of me how I did it.

Task is to have a menu of pages, and in that menu have a page with maybe for sub pages. Each with it’s own template to display specific category postings like a normal blog would with image and description with read more or something.

Home
About
For Sale
– Horse
— Display all ‘horse’ category posts
– Dog
— Display all ‘dog’ category posts
– Cat

I remember it being something like is_page or is_cat. I just can’t find anything similar on google. I’d simply like to be able to somewhat crudely display the listing of posts like it would normally show up, just on a page since the template functions like that.