Well, the original tanks (such as the British Mark series) were intended to be exclusively infantry support. These were rolled out (pun 100% intended :D ) during the first World War as essentially (hopefully) big chunks of metal for infantry to hide behind as they advanced across the no man's land in between trenches. They were practically impervious to machine gun fire, and when used in large numbers they were indeed quite effective. Unfortunately, they were also really slow (the first tanks moved at the pace of a walking man, and even the tank that many consider to be of the first "modern" tank design [a French vehicle named the Renault FT, or FT-17] was considered fast for being able to move at the pace of a jogging man). They were clunky, they were HUGE (the Mark I was 26' long (7.62m)), and they had lots of mechanical failures. If you're interested in learning about particulars of WWI tank warfare, I recommend looking up the Battle of Cambrai. It is often considered one of the best displays of the advantages tanks offered to infantry in WWI (cover from enemy fire, the ability to just roll through barbed wire [and clear it for infantry to follow], and of course the simple intimidation factor of almost 400 of these mechanical monsters rolling down the field of battle to you).

Now, to more specifically address your question, the difference in the effectiveness of vehicles in WWI as compared to WWII is quite simply the advances in technology that were made in between the two wars. "What made vehicles effective in the infantry support role," is exactly what made horses effective in that role pre-WWI (and even during WWI). Automobiles were not that widely used yet by the time WWI kicked off. Until the powers started laying railroad tracks down in the war (to their more highly fortified defenses/staging areas), almost all supply trains consisted of horse powered transportation. Not only that, but these militaries still had cavalry divisions! The advantages of the much more efficient vehicles that were available for use in WWII, over their WWI four-legged counterparts, were astronomical. Vehicles were effective in infantry support because what they replaced had also been effective in infantry support (in the past), except that what vehicles replaced (horses) were absolutely slaughtered in modern combat. Cavalry was rendered almost completely useless in WWI, let alone WWII (see the Polish cavalry vs. the Nazi-German Blitzkrieg). Not only did vehicles bring back the ability to move troops and arms (on and off the battlefield) quickly and nimbly (depending on who's driving :D), but they were more effective at it than cavalry ever had been. Throw some big guns, some all terrain treads, and the tons of steel used to make them (perfect for hiding infantry behind in a fire fight), into the mix and their advantages are quite apparent.

Now, while yes tanks were originally designed as infantry protective (and even, in some cases, infantry fighting) vehicles, it quickly became apparent that there was nothing quite as good at blowing a tank up... as another tank was. Artillery and anti-aircraft weaponry, of course, were effective at taking care of most tanks of the time (and in fact, the only weapon that the German's had that could reliably destroy or immobilize the Soviet T-34s at range [when/shortly after they were first encountered, at least] was their 88m anti-air flak cannons). Sure, artillery and other mostly-stationary weaponry (such as anti-air cannons) could destroy tanks, but tanks could move faster and could shoot back. And while you were worried about the tanks, there were soldiers on the ground, and maybe even planes in the sky. As the ideas and strategies of how to implement this still sort-of-new concept of "Modern Combined Arms" continued to develop, tanks continued to develop with them. In WWI, only Britain and France had any meaningful number of armored vehicles, by WWII all the major players had tanks. In a time when everyone had them, they had to start developing them to be able to deal with their counterparts that were under the enemy's control.