When we say that a hypothesis is an “idea on trial” we mean that it has been proposed as an explanation for something but has not yet been confirmed or proven. Thus, the idea is “on trial” as we try to determine whether it really is accurate. This is part of the scientific method that is used both in the “hard sciences” and in the social sciences.
A hypothesis is a proposed explanation for some phenomenon whose causes are not yet known in a scientific way. For example, Darwin once hypothesized that the differences in various animal species were caused by natural selection. At the time, there was no scientifically proven cause for this and Darwin was proposing one. Social scientists hypothesize as well. For example, in the wake of the shooting in Connecticut, there are various hypotheses as to why such mass shootings occur. Some hypothesize that it is because of the easy availability of guns. Others propose that violent video games and other media cause it. Still others propose that a lack of mental health programs is to blame. None of these has been proven to be correct.
In the case of Darwin, his hypothesis was put “on trial” and was eventually proven. Now it is no longer a hypothesis. The social science hypotheses have not yet been (and my never be) tested. They are still “on trial.”
So, what this quote means is that a hypothesis is an idea that has been proposed but not yet accepted. It is still “on trial” through observation and experimentation to see whether it is a good way to explain a particular phenomenon.