The Cox model is a statistical technique to analyze the chance for some event (ie. live birth) to occur over time. It can be multivariate, and include different variables to look for independent associations (see the glossary term for univariate and multivariate regression analysis for more info).
It uses a “hazard ratio” (which I’ll describe as “chance” for simplicity) to estimate how different factors can increase or decrease the chance of an event happening. More accurately, the hazard ratio is a statistic that shows the “risk” of an event (like live birth or pregnancy) in one group compares to another group, over time.