You do NOT need to install a third party app.

Both Google Chrome and Firefox support this functionality. (ok, technically these are third party apps, but lets assume you are not using safari.)

Chrome:

1. Open gmail in chrome.
2. In the address bar next to the "bookmark star" you should see a grey diamond. Click on the diamond
3. Select "use gmail".
4. If you do not see the gray diamond, follow the instructions below.

If you made a mistake and selected "No" and you really wanted to select "Use Gmail"

1. With Chrome open, copy and paste this into your address bar at the top: chrome://settings/handlers
2. Under the Ignored protocol handlers section, Click on X to the right to delete.
3. Close and open Gmail.
4. Answer the question correctly this time. :)

Source: http://productforums.google.com/forum/#!topic/chrome/hnRteY7bHfE

Alternative way, if you need to do this programmatically.

Firefox:

See @Am1rr3zA answer on this question. Click here to jump to his answer.

Safari:

See @fpotter's answer on this question. Click here to jump to his answer.

You can use multi-touch gestures to swipe to the last app you used, in this case will be mail.

First make sure Multi-Touch gestures are turned on in the settings panel.

Once this feature is on, you can swipe from right to left with four fingers or more to cycle through the apps you last used.

If you do not want to use that, you can double tap the home button top bring up the last few apps used.