Logistic regression yields adjusted odds ratios with 95% confidence intervals, rather than the more prevalent unadjusted odds ratios used in 2x2 tables. The odds ratios in logistic regression are "adjusted" because their associations to the dichotomous categorical outcome are "controlled for" or "adjusted" by the other variables in the model. The 95% confidence interval is used as the primary inference with adjusted odds ratios, just like with unadjusted odds ratios. If the 95% confidence interval crosses over 1.0, then there is a non-significant association with the outcome variable.
Adjusted odds ratios are important in medicine because very few physiological or medical phenomena are bivariate in nature. Most disease states or physiological disorders are understood and detected within the context of many different factors or variables. Therefore, to truly understand treatment effects and clinical phenomena, multivariate adjustment must occur to properly account for clinical, prognostic, demographic, and confounding variables.