Is there any website or journal that publishes most significant recent studies and articles in psychology? I have access to EBSCO database, but there are thousands of articles and most of them of almost no importancy and I have no idea how to find those good and important ones.
By definition all journals publish "recent studies" because they are publishing all the time (either on a monthly/qaurterly basis). Sometimes, journals publish articles online months before in print. However i think your question is about finding the best articles, rather than journals, and there are a few tricks.
If you have access to any good search engine (google scholar, web of science, scopus), you can perform searches in there, and then rank articles by number of citations. This will give you the most important and talked about studies, although by nature they will be quite old studies, since in order to be the most cited they have to be out for a while.
Another good trick is to use webofscience / webofknowledge feature which lets you look at articles that have cited a specific paper. Say you find a classic study that you want to find more recent research on, webofknowledge will let you find recent studies that have cited that paper.
Alternatively a good place to start is looking through review articles or textbooks first. You can find these by adding "review" to your search terms, e.g. ("Social learning" AND "animals" AND "review").
Finally, looking at the web pages of important researchers in a given field would be a good place to find recent research, usually they will have fairly up to date lists of their recent research If you've done a bit of reading then you should be able to identify key researchers in a given field.