Mint, unlike some other distros, assigns "security levels" to all updates. Synaptic/apt-get don't do such things and update everything which is why you might end up messing up your system with unsafe/unstable packages.
Now, with "visible" and "safe" you can define which levels of updates you want to SEE in MintUpdate (visible) and which ones you want to have automatically updated (safe).
Everybody recommends that you only check level 1, 2 and 3 as "safe" although if you're curious you might set levels 4 and 5 to "visible" to look what is available in the unstable repos. Marking 4 and 5 as "safe" is generally not recommended for normal usage.
War does not determine who is right - only who is left. - Bertrand Russell