I think what historical contextualization means to your professor is situating your texts in the relevant historiography. Whatever subject they're speaking to, it has a historiography. Trends in academia, wider world stuff, new findings, and so forth place their stamps on generations of scholars who then react to their predecessors and then are reacted against by their successors. All of this usually leaves distinct patterns where older work shapes newer, but also gets revised in different ways and with shifting emphases over time. Understanding the big picture can help you suss out the strengths and weaknesses of individual works as well as making them somewhat more intuitive all on their own.

So how do you do that? The standard answer is "too much reading", which is probably not too helpful for you. :) It's hard to explain after having done it for so long, but you begin with basic questions like: When was this work written? What was going on around that time in the world that might have influenced the author, and maybe for a few decades before as they're growing up? What kind of evidence (statistics, primary sources, kinds of primary sources) does the author stress? Does the author treat one group of historical actors more favorably or adopt their framing of things more than they do another group? Is a group concerned with the subject and involved in events conspicuously absent? If you're an American, look for Americans who aren't white men.

The ways those questions are answered gives you some of that context. For example, a history of American slavery written in the 1910s is the product of a time of intense and violent white supremacy. We might look askance at its depiction of the slaves as largely content and benefiting from the institution. One written in the 1950s or 60s, by someone cognizant of the Civil Rights Movement, might look at the same data and come to a very different conclusion. (And did they ever.) Historical works don't ever stand on their own or descend unto us from the heavens, they themselves are the product of history just like the historians who produce them. Contextualization is part of how we account for that.

Textual interpretation is also a little hard to explain without doing it. I think what your professor will be looking for is a close examination of how your historians use primary sources. If they have a long quote, then they probably have an interpretation right before or after it. On a larger scale, every historical work involves textual interpretation. Do the quotes and sources support the argument? Are there other reasonable ways to read the texts quoted? Are the historians missing, or outright ignoring, a credible read that runs contrary to their argument? If you have a source document on hand (or can get it online) then you can read the whole thing and see if the interpretation is supported by it in general. Many a historiography note involves a prior scholar selectively, incompletely, or incorrectly reading something. Occasionally they're downright vicious.

Let me give you an example of the job being done:

One of the most knowledgeable historians of the period, Robert V. Remini, for example, discounts the significance of the slavery issue in Van Buren’s formulation, noting that “the issue of slavery was never seriously raised” during the election of 1828, and citing a comment by the Jacksonian editor Duff Green: “The anti slave party in the North is dying away.” 18 But this simply demonstrates that the policies promoted by Van Buren, Ritchie, and Calhoun to replace “party feelings” for “geographical divisions” were working— just as Green observed in a portion of the same letter that Remini did not quote: “It has been a part of my business so far as I could to prevent the agitation of that question.”

Forbes, Robert Pierce. The Missouri Compromise and Its Aftermath: Slavery and the Meaning of America (pp. 214-215). The University of North Carolina Press. Kindle Edition.

Robert Remini was Andrew Jackson's biographer and loved the guy. Forbes went back to the letter Remini quoted and found material within it that didn't support Remini's argument at all. He wants Green as an authority on how antislavery sentiment has withered a way, so it doesn't matter anymore but other issues Remini cares about do. To get there, he chose to ignore Green's admission that he was literally working to suppress antislavery and so take it off the menu. Forbes concludes:

One is at a loss to know just what contemporary politicians would have had to write in order to convince Remini and others of his school that slavery represented a central issue, if not the central issue, of national politics at this time.

Forbes, Robert Pierce. The Missouri Compromise and Its Aftermath: Slavery and the Meaning of America (p. 215). The University of North Carolina Press. Kindle Edition.

I'm not personally familiar with Remini's work except that he was the dean of Jackson scholars for a long time and his three-volume biography is thoroughly laudatory. I am more familiar with the work of a recent scholar in that tradition, Sean Wilentz, and find his interpretations pretty poor. Many in the academy agree, to the point that the best general survey of the era, What Hath God Wrought was essentially written to displace his work The Rise of American Democracy. I read both almost back to back because I am very boring want to see for myself and in the process caught Wilentz in a few dubious interpretations of his own that I wouldn't have noticed if not for having read WHGW.

This must sound like a lot of work. It is. But unless you're in graduate school I doubt your prof expects you to know the historiography and be able to take Sean Wilentz to the woodshed. (If your prof is Sean Wilentz...maybe don't do that. :) ) The goal is almost certainly for you to start developing these skills, which will eventually become second nature as you get further into history, if you do press on.

What you might find helpful to get started are some good historiography reviews. They're most helpful if you're studying American history, but Eric Foner writes great historiography in both Reconstruction and Gateway to Freedom. Each is a capsule history of the relevant field all in itself (and the second edition of Reconstruction has a second one to update the first). Foner has the rare gift of making the review genuinely entertaining, which is probably why they survive his editors.