how do I update my MacBook Pro browser?

If you're running Safari 5.1.10, you need to either upgrade the OS or use a different browser, such as Firefox or Chrome.

If you're running an earlier Safari version, check for updates in the Software Update pane of System Preferences.

If you're using a different browser, check for updates from within it.

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To update Safari you need to update the OSX version.

Go to the Mac App Store and see if an update is available for your model Mac. Some can can only go to 10.6, some to 10.7 and some to Yosemite.

I can't say since you did not identify your model Mac Book.

BTW, this is the Mac Pro desktop forum