Without more information about what monitoring tool you're using and exactly what it's showing, it's hard to say for sure what's going on. But I can tell you a little bit. mDNSResponder has three main jobs on OS X:
Sending out multicast DNS (mDNS aka Bonjour) lookups to the local network on port 5353 (and listening for responses). These include both looking up names (e.g. "I'm trying to contact somethingorother.local; what's its IP address?") and looking up available services (e.g. "what computers on the local network provide AFP file sharing services?").
Listening for and responding to mDNS lookups that apply to it. For example, if its Bonjour name is xxxs-MacBook-Pro.local and it sees a request for xxxs-MacBook-Pro.local, it'll reply with its IP address(es). Similarly, if you have AFP file sharing turned on and it sees a request for AFP servers, it'll reply ("Me! I'm xxx's MacBook Pro and I provide AFP service on port 548!").
Sending out normal (unicast) DNS lookups on port 53 to some DNS server (and listening for responses). Names that end in ".local" get sent out via mDNS; everything else (e.g. "www.apple.com") gets sent via normal DNS to the server(s) configured in the network settings.
If you're seeing activity on port 53, that's normal DNS. I'm not sure why you're seeing it as an incoming connection (unless it's really a reply to request you sent out?), or why the source would be your own computer. For those, I'd need more detailed info about what you're seeing.