when it appears a message " someone is scanning your pc" ..what it means?..it means some enter the pc?...and should i turn off the internet?..or can i stay turned on? thanks..

it means sygate detected someone was scanning your computer, probably going down a list of ports to see if they're open. Since sygate caught it, you have nothing to worry about. It just means it detected that someone is probing the computer for vulnerabilities, but didn't get through (since your firewall blocked it and reported it to you)

Don't worry about that. What you are seeing has been around for years. A real concern would be an outbound connection attempt which would most likely indicate you having a trojan. What you see there is everyday Internet background "noise". Usually when a person get their first firewall setup they get startled by all the apparent attempts at cracking into their computer. Not so! This happens to everyone online, but only users with firewall detect these mostly harmless irritations.