Why can't I download anymore apps on my iPad?
As noted in another answer, you'll need to remove some data if you want to install new apps. What you remove really depends on what's taking up lots of space — it might be apps (games in particular tend to be large), videos or music.

You can get a good overview of what's taking up space on your device by going to Settings → General → Usage. You should see a breakdown of how much storage each app is taking up. You can also remove apps from this screen, or if tap on the Music or Videos apps, you have the option of removing some media files more granularly.