The most important thing in evaluating for relevance to your specific research project is to be clear on what your research question is. What are you trying to find out about your topic?
What is the scope? How broad or narrow is it?
For example, your topic is learning disorders and your research question is, "What are some common learning disorders in elementary school-aged children?"
The following research articles are probably too specific and too narrow to be relevant
Enumeration of Small and Large Numerosities in Adolescents with Mathematical Learning Disorders
A Longitudinal Study on Gross Motor Development in Children with Learning Disorders
Comorbidity of Learning Disorders: Prevalence and Familiar Transmission
What is the focus? What aspect(s) of the topic does the source address?
Consider where the source is talking about--excellent articles about teachers helping kids with learning disorders in Spain or Ghana won't be relevant if you want to find out how NYC schools help their students.
Consider who the source is talking about--fantastic articles about pre-K children with autism won't be relevant if you want to find out about good strategies for high school students.
Consider the aspect of the topic the source is talking about--great articles about how the Americans with Disability Act has affected teaching policies about learning disorders won't be relevant if you want to find out whether kids with dyslexia are more or less likely to have auditory processing challenges.
When was it written?
If you are looking for the most recent and up-to-date research on treating Alzheimer's disease, a research article from 20 years ago will not be appropriate and relevant.
For many of your research projects, you will be looking for recent materials, but some fields change faster than others.
For instance, changes in mobile technology are happening so fast that something written just three years ago will be out of date.
However, a 1990 critique of a political philosophy or 2001 historical account of a 16th-century war might still be considered important or relevant within the fields of political science and history. (Keep in mind, however, that scholarly discussion in those fields does change over time, and scholars also respond to and build upon the work of each other, so you would also want to find relatively recent work.)
Primary sources are also a big exception to the idea that something is more relevant if it is more recent. If you are looking for first-hand accounts of the Newark Rebellion in 1967, a 1967 newspaper article would be very appropriate and relevant. If you want to read the original writings of Charles Darwin, of course, these were written when he was alive.
What if I am unsure if the source is relevant?
This often happens at the beginning of working on an assignment, and most often the real problem is a lack of clarity about the research topic and question. For tips on choosing and narrowing a topic, visit Getting Started with Research or come talk to a librarian.