In the informal meeting, Alex first thanks Shawn for organizing the meeting.
He says, "We all appreciate you telling us about the work that your team has done."
"To appreciate" (appreciate) means to feel grateful or thankful for something.
"I appreciate you coming here" means "I want to thank you for coming here."
Alex then says that "The new committees have a lot on their plate (plate) over the coming weeks and months."
"To have a lot on your plate" means to be very busy, to have a lot of work to do, or to have many responsibilities.
If you say "I have a lot on my plate right now," you mean you have a lot to do; you have, perhaps, too much to do.
When Alex says the committees have a lot on their plate over the coming weeks and months, he means the committees have a lot of work to do.
The word "coming," here, means something that will happen in the near future.
The "coming weeks and months" means the weeks and months that are near to us in the future.
The coming weeks and months, then, are the ones that are coming soon.