Imagine the Mediterranean sea as a crossroads. The East-West road runs from Gibraltar to Egypt. The North-South Road runs from Italy to Libya (and Tunisia). Malta sits at the center of the crossroads. The British needed to move supplies from the Atlantic to Egypt, the Axis from Italy to Libya, whoever controlled the sea around Malta would get to use their "road" and deny the enemy the use of the road they needed. Malta's importance in 1940-42 was that air bases on the island had the potential to contest or control the sea lanes in the area (submarine basing was also important).

As for why there was no invasion, that is complicated and difficult to answer at a reasonable length, since Malta could have been invaded at quite a few times between 1940-42. In short, neither Germany nor Italy had a reliable amphibious doctrine (or airborne doctrine after the expensive Crete campaign) that they felt could secure them the island cheaply. They felt they could more easily secure the sea around the island of Malta by air and sea attacks from the mainland and aerial bombardment of the island itself.