There are two Mojang server that are used for authenticating Minecraft accounts in order to verify that a connection from a particular ip is actually the Minecraft username it says it is:

(1) The Login Server
The login server checks a username and password to see if they match Mojang's records (hopefully against a salted hash but I haven't actually checked).

(2) The Session Server
The session server keeps track of who is logged in, in order to tell a server that a particular 'session' is a particular account without the server knowing the account password.

Sometimes, one or both of these go down for some amount of time.
Case (a): If the Login Server is down but the Session server is up then as long as you don't close your minecraft client you should still be able to connect to server, however you cannot generate a new session so if you aren't logged in you out of luck. Case (b): If the Session Server is down but the Login server is up, then you are able to login to minecraft but you are going to have difficulty connecting to minecraft servers, sometimes you will be able to connect but sometimes not, it will often take a long time and require many attempts.
Case (c): If they are both down then you are up a certain well known creek without a paddle.

Case (b) has been happening a lot lately and many people have attributed these problems to some kind of DDOS attack on civcraft. It may be the case that someone has attempted to DDOS the server civcraft is hosted on (and if so not very effectively) but this particular problem is not caused by a DDOS.