What do the blinking lights inside the case mean?

For blue, likely no. Regardless though, it depends where the light is coming from. If you have no problems, then it is likely that they are just status indicators or for aesthetics. One exception would be the motherboard's LED error indicator. If you do have issues, the first place to look would be here. It settles on a code after booting up (or failure to boot up). After determining the code, you would then be able to check either online or within the manual (for the specific motherboard) to determine what the code is telling you.