Implications of changing compatibility mode in SQL Server from 100 to 110

Have a look at the following link:

ALTER DATABASE Compatibility Level

Scroll down and you will see the section "Differences Between Lower Compatibility Levels and Level 110" and identify if any of these items will affect you or not. If not, then just change the level to 110.

Microsoft Data Migration Assistant helps you quickly and easily find any issues that may prevent or complicate an upgrade.

If it finds no issues (or if it does, and you've addressed them) you can simply upgrade by running these commands, one at a time:

USE master
go
ALTER DATABASE [yourdatabasesname]  SET SINGLE_USER     WITH ROLLBACK IMMEDIATE
go
ALTER DATABASE [yourdatabasesname]  SET COMPATIBILITY_LEVEL = 110    -- 130=SQL Server 2016, 120=2014, 110=2012
go
ALTER DATABASE [yourdatabasesname]  SET MULTI_USER
go

There is also the Upgrade Advisor which will help you identify anything in your DB which might cause problems when changing the compatibility level (basically a semi-automated way of doing what @steoleary has suggested which reduces the chances of you missing anything).