People that search are much more likely to convert than people that just browse, because they are better engaged since they actually interacted with your website by searching for a specific product, category or brand.
To illustrate why personalized search will improve the user experience and conversion rate on almost any site, we can consider this example:
Let’s say I own a small townhouse with a front lawn, but you own a large mansion with a yard and gardens. I’m looking for a small electrical lawnmower and you might be looking for a larger riding mower.
If we both go the same e-commerce site and search for “lawnmower”, we would often be presented with the same products. If the on-site search engine displays regular petrol push-mowers, neither one of us will be very happy with our first search. We might even leave the web shop and go looking for our lawnmowers somewhere else.
With personalized search we would each be presented with a lawnmower in the category that we are looking for, making us less inclined to leave, but more inclined to make a purchase.