On the far left of each row there is a gray box in front of the first field (the gray row box always remains visible, even if the fields scroll when you go to the right end of the row). If you double click one of those boxes you will be zoomed to the feature matching the row you double clicked on if the table view is for a Feature Class or a Shapefile.
If you right click inside that box a context menu will appear. If the Table View is for a Feature Class or Shapefile, at the top of the Context Menu list is Zoom To, which will zoom you to the row you right clicked on when you left click that option.
If there are selected rows, in the center of the Context Menu there will be an option to Zoom To Selected Features (or something to that effect). If you click on that option you will be zoomed to the records you have selected.
If you are in Show Selected Rows Only mode in the table and have highlighted some of your selected rows, toward the bottom you will have the option to Zoom to Highlighted Features. When you left click that option you will be zoomed to the highlighted features.
There are also several keyboard shortcuts for interacting with the map from the table, like Ctrl+Shift+= to zoom to selected features.
