Many things can be cleared by going to your Recently Viewed page and using the "Clear all" link.
But some things that appear on the main eBay page are the result of Saved Searches and Saved Sellers -- those will remain. You can unsubscribe from those searches, or use your Feed page to select which searches or sellers contribute to your feed. The "Saved" link on the main eBay page in the upper left leads to your Feed page. From there click on the number of saved searches or saved sellers to reveal a drop-down menu of those lists and use the sunglasses icon to reveal toggles that control whether those searches contribute to your feed.
Some things shown on the main eBay page are the results of past searches; those can be displaced by performing new searches.
The last four items viewed also appear on your Purchase History page; those can be displaced by viewing new items.
