Global thresholding works by choosing a value cutoff, such that every pixel less than that value is considered one class, while every pixel greater than that value is considered the other class.
ImageJ provides several built-in methods for automatically computing a global threshold. For details, see:
Local thresholding techniques adapt the threshold value on each pixel to the local image characteristics.
The ImageJ Ops project provides algorithms for both global and local thresholding.
How do I know whether my threshold is correct?
In short, you can't. It will always be, to some extent, in the eye of the user/observer/scientist and will also be impacted by empirically collected knowledge. The basic problem of deciding if a threshold (or in general an extraction method) is "good" needs a "ground truth". But such a ground truth is not naturally existing and is always created in one or the other way by a human. So, describing which method you use—and/or showing a comparison with other methods—is probably the best you can do to enable a statement on the quality of the extraction.
For more detailed information on thresholding and image segmentation basics and some quality evaluation see the Principles page.