If you've been blocked by someone on Instagram, you won't be able to see their photos or videos. If you try to view a blocked person's profile, you will receive a message saying Sorry, this user is private. If the person who has blocked you is someone who you are following, their name will disappear from your list of followers. If they are not somebody that you are following, their profile will still appear in search results, but you won't be able to view their photos or videos.
If the person who has blocked you is someone who you were not previously following, then their profile will still show up in search results and you can still see their username. However, when you try to view their profile it will say User Not Found. Additionally, if somebody blocks you and then unblocks you at a later time, they will reappear on your list of followers (if they were already following you) or as a suggested follower (if they weren't already following you.)