In World War II, warfare was fought in three domains: the tactical, the operational, and the strategic levels. The tactical level is what we are most familiar with, which is to say, the art of actually fighting a battle. This could be anything from using artillery to shell or smoke a position, using infantry to storm or garrison an area, using tanks as fire support as to hunt tanks, moving this regiment here, sending this battalion there, and so forth.

Then there is the strategic level, which is to say, the conduct of the war as a whole. Where do we attack, how do we knock out the enemy's ability to fight, how do we process military industrial production, how do we process our conduct in this theatre, and so forth.

Lastly there is the operational level, which is to say, the ability to manage different tactical groups. This could be anything from deploying reserves, targeting communications lines between headquarters and the front line, capturing enemy supply depots, and so forth. In effect, it is about breaking the ability of the enemy's military to operate.

The German military never really recognized the last of these three concepts-their focus was primarily on the tactical and the strategic levels. As far as they operated, divisions and smaller units would operate on the tactical level, while armies and army groups would be managed by generals looking at the strategic level.

Rommel's initial claim to fame was when he was a divisional commander, having been one of the first divisions to cross the strategic barrier of the Meuse river in France (although a good chunk of this was due to Nazi propaganda, as his breakthrough was not the most decisive of the German crossings). He managed his division well and this was part of the reason why he was sent off to North Africa against the British. In Africa, while he was assigned the 5th Light Division and the 15th Panzer Division, his initial success was based on taking the 5th Light Division and making a rapid advance (much as he did in France with his 7th Panzer Division) while the 15th Panzer Division was still unloading and not battle ready. This was despite the fact that he was a corps commander and no longer a divisional commander.

His success against the British soon quickly resulted in him outpacing his supply lines. As a corps commander, this was his responsibility, and his failure to organize them properly instead of taking one of his divisions and running at full speed across North Africa was a sign of what would be a common theme of his campaigns: tactical success against the British forces would lead to major logistical issues due to his failure to properly prepare and organize his forces. Despite driving superior British forces back several times and capturing the heavily defended Tobruk after a series of back-and-forth battles, Rommel continually had supply issues and did not properly manage the other German and Italian forces that were not directly under his command. Instead of utilizing the Italians and incorporating them into his command structure, Rommel lied to them on multiple occasions and basically forced them into following him without proper preparation or any real cooperation. The end result was that Rommel found himself at El Alamein with a fraction of the men and tanks that he should have-and this is after a streak of German victories. He simply did not manage more than a divisional unit to the same degree, whether that be due to disinterest or incompetence.

Specifically, Rommel was excellent at understanding what he had to do in a particular moment, in order to win the battle of the day. This skill came in useful time and again, especially at places like Kasserine Pass and (against the British) Gazala. On the battlefield, I would argue Rommel had few equals. His use of terrain and weather was second to none. It was not uncommon for Rommel to order attacks at night, in sandstorms. For a bit of an overview, see Rommel and His Art of War.

Now, despite Rommel's general competence on the battlefield, he was not particularly good at long-term planning, that is, strategy. Logistically, the Afrika Korps suffered supply issues that it really should not have. For example, Rommel's aggressive counterattack after Operation Crusader neglected the reality of supply issues. Beyond that, it didn't really have a defined objective beyond "drive the British back," which led to the counterattack ceasing far earlier than it could've. A good history of the Afrika Korps will probably cover this particular issue, see The Afrika Korps: An Organizational History, or alternatively Rick Atkinson's An Army at Dawn, which deals with the aftermath of Operation Torch.

Similarly with his preparation for D-Day, actually. As far as I can tell, the plan essentially was "repel the landing," which is all well and good, but you have to have an actual plan once the landing occurs. Rommel didn't, which led to elite units (like the 6th Fallschimjager) being moved from duties as a rapid response units, which they were very good at, to being sacrificed as a static infantry divisions. Stephen Ambrose's D-Day is a good, fairly straightforward read on this topic, but a more in-depth book is The Devil's Garden: Rommel's Desperate Defense of Omaha Beach on D-Day.