That would count clicks, not conversions such as downloads or signups that can require going on another page or doing some other action. Not everything can be put on one page.

Also, Google Adwords counts conversions for visits for 30 days. Which means on the 1st visit from the ad campaign, there can be no immediate conversion (and that's OK). But if the same person returns to the website (not from the ad) and downloads/signs up that would be counted as conversion attributed to the ad.