If you didn't know, seasons last three months and contain a set of objectives that if completed grant you special stuff. To date, I haven't put much thought to completing them as they weren't very interesting but for me, Season 5 and patch 2.4.0 has changed that. To read more about...

I was wondering if you could get Haedrig's Gift on multiple characters. Good to know. I'll probably do Monk for the first round.
So, it's not exactly a glorified version of Campaign Mode? I've played a hell of a lot of that in the last year and feel like I'm done with Campaign mode for a long time.
I thought it was cool that you mentioned in the latest roundtable that you jumped in with a Witch Doctor. I was thinking of checking out the new-to-me stuff and the Witch Doctor was probably the first that came to mind. I enjoyed that class, perhaps mostly because of the summons.
Also, is a Season played alone or with others?
Greg: Seasons can be played with anyone to my understanding. For instance, each time I play I open my game to others and get people joining in with me, it's nice because you get bonuses for playing with more people.
Frankly it feels like they took some nods from Hearthstone and Heroes of the Storm in that Seasons are like quests. It gives you something to work against other than simply leveling your character to make them beefy. I like having things to accomplish and the end goal of collecting cool stuff that holds over is a really nice reward. Currently more than half-way through the 3rd set of objectives.
Travis: I plan on getting the gear bags but I am unsure which character I will open it for. The Wizard bonuses look incredible.
Awesome sauce! Well, I'm not sure how I feel about playing with strangers, but with friends, that would be sweet! How many others do you normally play with? You said you're playing with a Witch Doctor, how many other Witch Doctors do you play with? Would it be too weird to play with another (me)?
So, it kind of works like Adventure Mode's bounties and Nephalem Rifts? Campaign Mode had objectives, but it was basically story driven and since I've been through the story very many times already, I'm not interested in repeating it any time soon. If or when a new expansion comes, I hope that I could bypass the current bits of Campaign Mode that we have.
How many objectives are there? Do you finish all of them with one character and come back with another for more?
Sorry to bombard you with questions about it, but you have more experience with Seasons than anyone else I know and I haven't done any "research" into them. I just know they go for a few months, take a break, release a patch, and come back again. I also know you can get various items, but aside from that and what you've posted here, I know nothing else.
I do enjoy playing games with you guys. I enjoyed that one time you joined me while I was playing. I look forward to playing more games with you all.
Oh and I like that they've made it so pets are actually useful instead of just cosmetic. I have an astral dog, so it'd be cool to get in and see what it can do for me. Also, being able to get more storage space is always helpful. I got all that I could before the latest patch and had so much extra stuff, I ended up storing them on other characters.
Seasons are a game mode that uses a different set of characters. You can now import a character to be seasonal but it is stripped of items. In seasons you can compelte objectives in single player or adventure mode. I recommend adventure mode and using bounties and rifts to complete goals. A Season objective would be something like "level up the blacksmith to 10" or "collect 10,000" gold.
http://www.diablowiki.net/Seasons