this = este/esta/isto that = esse/essa/isso/aquele/aquela/aquilo
the difference is in the distance from your point of view to the object you are talking about Este/esta/isto should be used to talk about something really close to you, like an object you are holding or something around you for an example (these words should be used but they are not commonly used, instead we use esse/essa/isso for almost everything) Esse/essa/isso should be used when talking about something not that far but not that close. Example: Me traga essas laranjas aí/Bring me these oranges over there. Aquele/aquela/aquilo are for something far away, a distant house, an high mountain, etc
I try to explain it here: http://www.duolingo.com/comment/536217.
To save you reading all that, here's a summary: strictly speaking a word like "este/esta/isto" should mean "this" and a word like "esse/essa/isso" should mean "that". This distinction has mostly been lost in Brazilian Portuguese and sometimes Duolingo translations support that view and sometimes they are more strict. The net result is that native speakers are frustrated and learners are confused.