Posts from hashtags you follow will appear in the same way that the posts of people and places you follow do — the only difference is that in the far left corner, there's a clickable link to the hashtag page, as well as the Instagram user who posted the image. It's an easy way to find new people to follow and see things that wouldn't ordinarily have made their way into your feed.
And if you're not crazy about a post you're seeing but like the hashtag overall . . . make sure you tell Instagram that! Click on the three dots on the upper right-hand corner and use the dropdown menu option to say you want to see less content like an individual post that's pegged to a hashtag. Finally, you have the option to truly customize your very own exploratory feed.