Targeted analysis is substances that you want identify. Method identification of substances are based on the fragmentation profile and based on retention time of compounds compared with standard compounds. 

I would like to add a little bit to the answers.

Targeted analysis means that you are looking for certain chemicals only. You know how they behave (e.g., mass spectra, retention times). The main thing is that you will not see other chemicals, which are possibly present in the samples. A typical mass specttometric targeted analysis method is based on selected reaction monitoring (SRM) on a triple quadrupole instrument. In this system you would increase both selectivity and ans sensitivity by limiting the amount of measured data.

In non-targeted analysis, you would basically aim to see any chemical present in the sample (not possible to detect everything in practice). A typical mass spectrometric instrument for this analysis would be a time-of-flight (TOF) or orbitrap instrument. In a typical method you would be looking at e.g. protonated molecules using high-resolution and then measuring MS/MS spectra for identification. A big problem in non-targeted analysis is the data processing.

A non-targeted method would allow you detection of both known and unknown chemicals. Former are easy as you know how to find and quantify them. Latter are the difficult ones.

Non-targeted methods are becoming more and more popular as researchers have to look more widely e.g. for harmful chemical in environment or for biomarkers for diseases.

In addition to what has been outlined above, it should be noted that the increasing interest in developing non-target analytical methods doesn't mean that target analysis will be one day an obsolete science. New organics are manufactured and thrown into environment every year and needs to be mnitored. In this case target analysis will be more specific and favorable 

Untargeted approaches provide the most appropriate route to detect unexpected changes in metabolite concentrations; the aim is to maximise the number of metabolites detected and therefore provide the opportunity to observe unexpected changes. Hundreds to thousands of metabolites can typically be measured.

Targeted studies analyse a relatively small and specific number of metabolites, typically up to twenty metabolites. These metabolites are chemically characterised and biochemically annotated with established biological importance at the start of the study before data acquisition is performed. Targeted methods have a greater selectivity and sensitivity than untargeted methods. Quantification of the metabolites is performed through the use of internal standards and authentic chemical standards to construction calibration curves for each of the metabolite.

Martin Söderström , such a nice explanation. Thanks. Could correlate every word.