You would do this by creating a new data frame. In the new frame you would have your large map, and in the smaller data frame your more zoomed in map.
For ARC Quoted from ESRI: http://mappingcenter.esri.com/index.cfm?fa=ask.answers&q=881
Here is how you can create an inset map in ArcGIS:
In Layout View, insert a new data frame and rename it Inset Map. To do this, in the top bar under Insert, select Data Frame.
Resize and position the Inset Map data frame where you want it to appear on your map.
Copy and paste the feature layers from the main map's data frame into your Inset Map data frame. To do this, you can select all of the feature layers in the main map's data frame, right click and select Copy and then right click on the Inset Map data frame and click Paste.
Use the data frame zoom and pan tools to zoom to the area that you want to show in more detail at a larger scale.
Another element that you will likely want to include in your map is an extent rectangle. Extent rectangles are a way to show the extent of one data frame within another data frame.
To do this, first right click on the main map's data frame and click Properties.
On the Extent Rectangles tab, under "Other data frames:", select the data frame of your inset map. Click the arrow to move the inset map data frame to the column on the right hand side under "Show extent rectangle for these data frames:" to show an extent rectangle for the selected data frame.
If you would like to modify the symbology of the extent rectangle (the default is a red, 4pt line width box), click on the Frame button on the right hand side. Here you can modify the style of the extent rectangle that appears on the map.
You also have the option to create more than one inset map on a single map. Just follow the steps outlined above for each geographic region you'd like to display at the larger scale. You could then assign a different color for each inset map border, and then match the color of the extent rectangle to the corresponding data frame's border color.
In QGIS: (quoted from Adding Multiple Maps in QGIS Composer?)
You need to lock the features on your your original map first using the Item properties tab. There is a tick box for this in the Main Properties section. You then get QGIS looking how you want the overview map to look and then add it in using the print composer in the same way you added the first map (The "Add New Map" button).
The new map should show up how you want it to look and you can set it as an overview. In the Item Properties for your new map you should find an option for "Overview" (it's about half way down just under the "Show Grid" Option. You need to tell it that the Overview frame you want it to look at is the original map (usually "Map0", but you can set this using trial and error). You can set how you want the overview frame to look.
You can set the scale and extents of this map independently of the first.
You can also add in as many maps as you want.