When you search google it fingerprints your browser then attachs that to the other information it amasses from tracking your other activities from other websites.

By not giving them the search content you reduce what they know.

Scenario a) you search up particular health issues on google, for the US say “how do I know I’m pregnant” then you go to an online pharmacy (Walgreen is the big US one I think) and order “plan b” (anti pregnancy drug). Google doesnt even need to know from walgreens what you ordered it will infer a pregnancy test and/or plan b then from later activity

Scenario b) you use proxy and thus google knows nothing of your search, then you go to walgreens, for all google knows you ordered makeup or hayfever tablets.

Scenario a is or will be illegal in some US states - best not to leak it.

Not a perfect example, i can poke holes in it. The point is searches are usually sensitive info, keeping them out of the hands of the most egregious activity collator keeps more privacy then if you don’t. The proxy buries your senstive search in with thousands of others that can’t be attached to you