Infinite scroll is what you see on a lot of newer style web sites such as Pinterest, Google Image search results, many landing pages with a lot of products on a single page and other methods. Google’s John Mueller, Maile Ohye, and Joachim Kupke wrote a blog post explaining various techniques to make those types of pages more search engine friendly.
The issue with infinite scroll pages is that web crawlers cannot always emulate the human user behavior, such as scrolling down a page to load more items. If a web crawler cannot access your content, i.e., the content as you scroll down, you likely will not see that content in the search results. Google said that in order to “make sure that search engines can crawl individual items linked from an infinite scroll page, make sure that you or your content management system produces a paginated series (component pages) to go along with your infinite scroll.”
Faceted navigation is when the navigation changes on a page based on the filtering options offered by the web site. This is often seen on large e-commerce sites that let you filter products by color, size, price, and other specifications.
Google’s Maile Ohye and Mehmet Aktuna said faceted navigation is “often not search-friendly since it creates many combinations of URLs with duplicative content.”
They go on to explain techniques to communicate to Google what content is duplicate, how to find all the content within the faceted navigation and the use of nofollow, noindex, robots.txt and canonical tags to go about this.
You can read the technical post over here on faceted navigation.