Tobruk has a strong, natural, protected deep harbor. It is probably the best natural port in North Africa, although due to the lack of important nearby land sites it is certainly not the most populous - the city is effectively surrounded by a desert lightly populated with nomadic herdsman that travel from oasis to oasis. There are many encarpments (cliffs) to the South of Tobruk (and indeed in all of Cyrenecia, the Eastern half of Lybia. These enscarpments generally have their high sides to the South and their low sides to the North. This provides a substantial physical barrier between the north and south of Lybia in the Tobruk area.
To the south of Tobruk is the largest airfield in Eastern Lybia. This, along with the harbor and some interesting nearby terrain features and a new railline made Tobruk a location of strategically substantial signifigance during World War II. A ralline passes through to the south of the city that connects Torbuk to the east with Matruh and on into Egypt. To the West the railline takes a coastal route through Derna and down to Benghazi. The railline from El Alamein to Tobruk was built by the British Commonwealth during World War II.
At the beginning of the Second World War, Libya was an Italian colony and Tobruk became the site of important battles. Tobruk is strategically important to the conquest of Eastern Lybia (then the province of Cyrenecia) for four reasons. First, it is a strong, natural, protected deep harbor. This means that even if the port is bombed ships may still anchor there and be protected from squalls, so the port can never be rendered wholly useless regardless of military bombardment. This is substantially important due to the importance of supplies in a desert warfare campaign.
Tobruk was also strategically important due to the fact that it was heavily fortified by the Italians prior to their invasion of Egypt in November of 1940. In addition to these prepared fortifications there are a number of enscarpments (cliffs) to the South of Tobruk providing substantial physical barriers to any advance on the port. Tobruk is also on a peninsula, allowing it to be defended by a minimal number of troops. All of this made Tobruk easily defensible to a small number of troops (indeed the British used this to their advantage when the port was under seige). An attacker, however, could not simply bypass the defenders for if they did the ensieged would sally forth and cut off the nearby supply lines of the attacker, spoiling their advance.
But Tobruk is also strategically significant due to its location with regards to the remainder of Cyrenecia (about the Eastern half of Lybia). Attackers from the East (Egypt) that have secured Tobruk may then advance through the desert to Benghazi (aka Benghasi), cutting off all enemy troops along the coast (such as at Derna). This advance would be protected from counterattack due to enscarpments that are quite impassible (on a military scale) that run generally Tobruk-El Aghelia. And again, due to the importance of supply in the desert, getting cut off in this area amounts to rendering such cut off troops ineffectual. Therefore whoever holds both El Aghelia and Tobruk controls the majority of Cyrenecia.
Tobruk is finally strategically significant because about ten miles South of the port is the largest airfield in Eastern Lybia. This is significant due to the importance of air power in desert warfare (as the Gulf War might attest to).
Although not as much a reason for its strategic significance, the British Commonwealth built a railline from El Alamein to Torbuk during the course of the war. This railline is significant both for purposes of supply but also as a sense of pride to the British troops, as the railline was built through a little-populated, inhospitable desert.
Italian forces (and their native Lybian allies - about two divisions worth of the latter) invaded Egypt in November of 1940 but only sat just across the border in neatly organized camps along the Mediterranean. The British Commonwealth, based around the 7th Armored Division, a British and an Indian Infantry Division launched a justifiable, preemptive counterstrike codenamed Operation Compass in early December. This counterstrike involved the British pocketing two of the Italian camps against the Mediterranean forcing their surrender. This led to a general Italian withdrawal and a British Commonwealth advance. As Tobruk is a mere 100 miles or so from the Egyptian border it inevitably fell. Tobruk was captured by British and Australian forces on January 12, 1941.
Italy called on her ally German which sent its 15th and 21 Panzer Divisions and 51st Light Division. Italy also supplemented its forces in Italy with the Ariete and Trieste Armored Divisions. These forces, under Generalleutnant (later Field Marshal) Erwin Rommel drove the British back across Cyrenecia to Tobruk, laying seige to it until June 21, 1942 (see: the Siege of Tobruk) when Allied forces surrendered there after a failed attempt to relieve the fortress. After the Germans overextended themselves at the First Battle of El Alamein and then were defeated at the Second Battle of El Alamein Tobruk was recaptured on November 11, and remained in Allied hands thereafter.
For more information on the World War II conflict in the vicinity of Torbuk see the Western Desert Campaign.
A simulation of the battles surrounding Tobruk that might help explain its strategic significance would be Europa (wargame)'s War in the Desert.