Low testosterone ages a man. There are many reason for this - one of them is the Low Testosterone-Induced Rise in Insulin Levels - including increased inflammation. As men we think of testosterone as mostly the "muscle" or "sex" hormone, but it is much, much more than that. If you begin to lose your testosterone, you pay the price in many more ways that just simply losing your muscle mass and libido.
As it turns out, one of the key ways that testosterone protects us men is by "modulating inflammation", i.e. keeping inflammation in check. Runaway inflammation is the curse of modern living (from poor diet and excess calories and body fat primarily) and is a root cause for heart disease, cancer and autoimmune diseases. So low testosterone is a big deal as inflammation ages and damages tissues in many ways as the decades roll by and we will show examples of this below.
In addition, it should be noted that excessive inflammation can also affect Leydig cell function and reduce testosterone. One study states that "There is evidence from many experimental studies that IL-6, TNF-alpha and IL-1beta inhibit T secretion by their influence on the central (hypothalamic-pituitary) and peripheral (testicular) components of the gonadal axis." IL-6, TNF-alpha and IL-1 are molecules called cytokines that control inflammation levels in your body and they are all-important.
Can this inflammation cause the hypogonadism and early andropause epidemic that we see in Western societies? I don't know of any proof of that, but it certainly is in the realm of possibility. On this page, though, I want to cover what we do know much more clearly: that low testosterone is correlated with high inflammation and that testosterone therapy can lower inflammation levels. Below are some of the major inflammatory markers affected in this way:
1. Adiponectin. Adiponectin is not an inflammatory cytokine like all the other markers I will discuss on this page. However, I put it first, because it affects inflammation and is SO important, although the relationship is complex. But here is the key takeaway: as a man loses insulin sensitivity (usually through weight gain and other aspects of a modern lifestyle), adiponectin levels will begin to drop and testosterone administration raises adiponectin levels. 
2. Phospholipase D. In 2011, scientists discovered one of the major reasons that testosterone may keep inflammation at bay. It turns out that your T actually slows down the activity of an enzyme related to inflammation called Phospholipase D. 
3. IL-1. The is one of the "bad boy" inflammatory cytokines. (IL-6 and TNF alpha are other well-known inflammatory cytokines.) Of course, a little inflammation is actually a good and necessary part of the body's defense-against-invaders. But most chronic disease in Western cultures is related to the opposite issue: long term elevated inflammatory levels. IL-1 is one of the chief culprits in a number of conditions, such as rheumatoid arthritis, and researchers recently found that testosterone administration actually "inhibited IL-1 secretion".  By the way, IL-1 potently inhibits Leydig cell function and testosterone levels. 
4. TNF Alpha. The most infamous of the inflammatory cytokines is undoubtedly TNF alpha as it has been singled out to be the root cause for so many nasty medical conditions including cardiovascular disease. See my page on Natural TNF Alpha Inhibitors for some additional information. And testosterone therapy has been found to lower TNF alpha levels in an animal study on rats following heart failure. 
5. IL-6. Although this is not uniform, some studies show that testosterone administration will actually decrease IL-6.  IL-6 is associated with many conditions, including diabetes, certain cancers, Alzheimer's and arterial plaque, etc.
6. CRP (C-Reactive Protein). Most middle-aged and senior men reading this page will have prediabetes, Metabolic Syndrome or full-fledge type II diabetes. For men suffering from these maladies relating to loss of insulin and blood sugar control, low testosterone had been found to correlate with higher CRP levels.  If testosterone actually causes this state of affairs, this is very bad indeed. C-Reactive protein is now a common test given by doctors to measure systemic inflammation and it is very correlated to the risk for heart disease, Alzheimer's, and many other medical conditions.
NOTE: The above study found that testosterone therapy did not actually lower CRP values, so low testosterone may not cause low CRP. When you see all the other ways below that testosterone negatively impacta inflammation, one cannot help but be skeptical however.
Now the short term data, which I outlined above, clearly shows that low testosterone affects some of the pro-inflammatory molecules in the body negatively and that testosterone therapy can help significantly. However, keep in mind that the long term picture is much more negative. The reason? Low testosterone promotes several medical conditions that are known to be pro-inflammatory.
For example, one research summary wrote:
"We suggest that androgen deficiency is associated with IR [insulin resistance], T2D [type II diabetes], Met-S [Metabolic Syndrome], and with increased deposition of visceral fat, which serves as an endocrine organ, producing inflammatory cytokines and thus promoting endothelial dysfunction and vascular disease."  Basically, low testosterone generally ages a man and puts his body in a pro-inflammatory state that is very difficult to escape from.
Other researchers have made the same observation, nothing that testosterone seems to have a protective effect on your Beta cells (that make insulin) through controlling these inflammatory messengers. 
1) Eur J Endocrinol, 2007 May, 156(5):595-602, "The effect of testosterone replacement therapy on adipocytokines and C-reactive protein in hypogonadal men with type 2 diabetes"
2) Obes Rev, 2005 Feb, 6(1):13-21, "Adiponectin: action, regulation and association to insulin sensitivity"
3) Journal of Andrology, January/February 2005, 26(1), "Testosterone Administration Suppresses Adiponectin Levels in Men"
5) Clinical and Experimental Rheumatology, 1993, 11(2):157-162, "Effect of gonadal steroids on the production of IL-1 and IL-6 by blood mononuclear cells in vitro"
6) Endocrinology September 1, 1991 vol. 129 no. 3 1305-1311, "Interleukin-1 Inhibits Cholesterol Side-Chain Cleavage Cytochrome P450 Expression in Primary Cultures of Leydig Cells*"
7) Journal of Endocrinological Investigation, 2005, 28(11 Suppl Proceedings):116-119, "The relationship between testosterone and molecular markers of inflammation in older men"
8) Journal of Andrology, Jan/Feb 2009, 30(1), "The Dark Side of Testosterone Deficiency: II. Type 2 Diabetes and Insulin Resistance"
9) Cellular Physiology and Biochemistry, 2007, 20:847-852, "Effects of Testosterone on Cytokines and Left Ventricular Remodeling Following Heart Failure"
10) Nature Reviews Endocrinology 5, December 2009, "Testosterone deficiency, insulin resistance and the metabolic syndrome"