Muxes are locations at which services can be found. On traditional networks (DVB-C, -T and -S), these are carrier signals on which the individual channels are multiplexed, hence the name. However, Tvheadend also uses the term 'mux' to describe a source for multiple IP streams - so an IP address, in effect.

The columns have the following functions:
Play
Downloads a playlist file (M3U or XSPF, depending on your startup options) so you can tune to the mux from an external application.
Enabled
Whether or not the mux is enabled and thus available.
EPG
Whether or not to retrieve EPG information from the mux.
Network
The name of the network to which the mux belongs. Networks are defined in Configuration -> DVB Inputs -> Networks - DVB-S or ATSC, for example.
Original Network ID
The ONID is a code which uniquely identifies a network.
Transport Stream ID
The TSID is a code which identifies the network origination source or transmitter.
CRID Authority
The group responsible for the Content Reference Identifier for this mux. This is effectively a URL/URI to an authoritative source for programme data (e.g. series link).
Scan Status
Whether the mux is being scanned (ACTIVE), is planned to be scanned (PEND) or has reverted to idle scan (IDLE).
Scan Result
Whether there were any problems with the last scan of this mux.
URL
Mux URL.
# Services
The number of services found on this mux.
Character Set
The character encoding for this mux (e.g. UTF-8).
Interface
IPTV : the network interface/card on which the IPTV source can be found.
ATSC
whether or not this is an ATSC IPTV source.