The term "T-regs" is shorthand for "regulatory T-cells"--a subpopulation of T-cells which act to suppress immune system activation and promote tolerance towards self-antigens. Although the existence of T-regs was felt to be controversial up until relatively recently, the idea that such a subpopulation exists is now well-accepted, and it turns out that understanding the role of these cells may be invaluable in treating kidney transplant rejection.
In the field of immunology, it's all about the markers. Subpopulations of cells are defined based on the presence or absence of specific cell surface markers (such as CD4+ or CD8+ cells). Recent work has attempted to identify the markers which define the regulatory T-cell population: in general, T-regs are CD4+, Foxp3+, CD25+, and CD127-/low.
How do we know that T-regs exist? In one early experiment, Sakaguchi et al isolated CD4+ cells from a mouse, subtracted out the CD4+ CD25+ subpopulation, and injected the remaining CD4+ cells into a lymphocyte-deficient mouse, resulting in an autoimmune disease. They found that they could "rescue" the autoimmune phenotype by inclusion of the CD4+CD25+ subpopulation of cells with the rest of the CD4+ population, concluding that this subpopulation is capable of downregulating activated T-cells.
From a renal transplant perspective, it turns out that patients with stable allograft function tend to have high circulating levels of regulatory T-cells, whereas recipients with chronic rejection have fewer T-regs. Not surprisingly, this has led to the idea that we may able to better induce graft tolerance by enhancing the number or function of T-regs in a transplant recipient. A recent mini-review in CJASN by De Serres et al describes the effect of the currently used immunosuppresant medications on T-reg function.