From what I can tell, it appears that a pin on many of your parts is designated to be a POWER connection. This means that Eagle expects that pin to be connected to a Vcc from the supply1 or supply2 library.
If you are connecting power manually using a net not connected to Vcc, then Eagle will give you these errors as the expected POWER connection is not present.
It's just a safety check. In industry you would probably want to designate things properly and connect things according to specifications. In my board I sometimes have nets named 5V, 12V, etc.. and sometimes get these errors as the ICs are not connected to a Vcc (strictly speaking).
Basically pins in eagle schematic symbols can have different types (e.g. Input [
in], Output [
out], Power [
Any pin that has a type of Power, Eagle is expecting to be connected to a net with the same name as the pin (e.g. if the power pin is called Vcc, it expects it to be on a net called Vcc). If it is not, you will get a warning to let you know. These should be simply checked through (make sure the power pins are on the right nets) and approved.
power pins should only be used for power connections (e.g. VCC, GND, 5V, etc.). The fact that you are getting these warnings for the pins of your 7-segment display means that the symbol was not made correctly. Personally, I would edit the symbol and change the type to either passive [
pas] or bidirectional [