A multi-select is just what it says - the dispatcher selects multiple CCMs (channels or talkgroups) on their console, therefore, when the dispatcher transmits, they transmit on all channels and talkgroups they've selected. Imagine if you pick up two portables on different channels, key them both up, and talk into both of them. This is essentially what multi-selecting is.
Patching is when two channels are linked together, we'll say for example, channel 1 and channel 3 are patched together. Everyone monitoring channel 1 hears everything on channel 3, and visa versa.
Counties with a TRS that use a conventional channel for paging and dispatching will often have their TRS dispatch talkgroup and their paging channel "patched and multi-selected." The multi-select is so that the dispatcher transmits on both channels, and the patch is so that radios monitoring the paging channel can also hear field units transmitting on the TRS. Often times, such as in AA and Baltimore Cos, the recieve function on the paging radio is disabled, so there will be nothing heard over the TRS from the paging channel, even though they sre patched together.