In most cases, it feels like absolutely nothing.

Above roughly 150 systolic, it can start to manifest as headaches (as others have mentioned), but doesn't always.

In my case, after it had gone undiagnosed long enough (by an incompetent doctor), I had extremely severe headaches, constant nausea and vomiting, and vision problems that turned out to be capillary hemorrhages in my retinas. That was at around 240/120.

BUT: I am extremely lucky to have had all those horrendous symptoms. They alerted me to the severity of the problem, and caused me to escalate to a competent doctor. For many people who get up to that level of blood pressure, the first (and potentially last) symptom is a stroke or a heart attack.