Why are some updates called Important security updates?
How are they different from other updates?
Is my system insecure, If I don't install them?
How can there be very frequent security updates?
Does it mean my Ubuntu is very unstable or insecure?
What is a security update? How are they different from other updates?
Usually they are security-related bugs rather than new features or bug fixes. For example, it might fix a buffer overflow a developer found.
If I don't install them, is my system insecure?
Not necessarily, but there are exploits. If someone could manage to exploit them (which might not even be possible unless they have another exploit), it isn't totally compromised. However, you should assume that it is insecure, because if theres a slight chance that it is, for all purposes it is.
How can there be very frequent security updates? Does it mean my ubuntu is very unstable or insecure?
This comes into the differences between Linux and closed-source operating systems.
In Linux, security flaws are found much easier when they exist due to the code being open. Then the patch is immediately put upstream and onto your computer through the package update.
Whereas in a closed source system, often such flaws aren't found until exploitation. Its just a matter of when the security flaw is found, not the existence itself.
As the name says, security updates are important updates which will improve your security.
Some updates are only new versions of your applications with new features and some of them are bug fixes. Critical security bug fixes are included in "Important securty updates" in the update manager.
If you want your system to be secure you must install security updates as soon as possible. Without these updates, attackers may use vulnerabilities in your software to attack your system.
Also, it's a good idea to make Ubuntu check for updates daily and install security updates without confirmation: