A big turning point in my opinion.
For the British they finally got their 'winning' Commander, Montgomery.
For the Germans, the famed Afrika Korps.. and Rommel were beaten.... furthermore Scruff you can mention how this fact and Rommel's illness got him switched to building up the Atlantic fortress - a major concern for the Allies to pull everything together in the highest methodology possible to crack it open. This enhanced the Allies HQ abilities dramatically in my opinion.
For the Americans, major military shake-up with the humiliating defeats at Kasserine Pass. Hello Patton
Western Allies now had confidence they could win - and attack finally!
For the Axis they now had to shrink their frontage and go on the defensive in the soft-underbelly front of Mediterranean Europe.
Denial of the German attempt to control Egypt and thus the serious consequences of interdicting Allied supply routes from this area to the Far East Asian Front were nullified.
As BG mentioned, denial to the Axis of mid-east oil via an attack from Egypt was a crucial phase.
As mentioned the American landings were another step in developing amphibious assaults later in Sicily and Italy.
Actually Italy didn't surrender after defeat in North Africa, in fact they surrendered after Sicily's invasion and a couple of months after Mussolini was done in... Though they lost much of their army in N.Africa a few elite units were still fighting alongside the Germans in Sicily, and many times more non-Elite ones... here's an excerpt of how big the Italian forces were at this stage after the mass surrender of many Axis units in Tunisia '43;
from here;
http://www.army.mil/cmh-pg/Brochures/72-16/72-16.htm"Although Allied planners opted to concentrate their ground forces in the anticipation of tough Axis resistance, the actual combat capability of Axis troops deployed in Sicily was questionable. Axis forces consisted of between 200,000 and 300,000 Italian and about 30,000 German troops under the overall command of General Alfredo Guzzoni's Italian VI Army. The Italians were organized into six coastal divisions, four infantry divisions, and a variety of local defense forces. Many of these units were woefully deficient in equipment, training, and morale and would prove incapable of putting up serious resistance. In fact, many Italian soldiers were tired of Mussolini's disastrous war and would surrender at the first opportunity. The German troops were divided into two divisions, the 15th Panzer Grenadier and the Hermann Goering Panzer. They formed the hard core of Sicily's defenses. The 15th Panzer Grenadier Division was essentially combat ready, but the Hermann Goering Division was significantly understrength and contained some inexperienced personnel."