The original expectation was to gradually increase the block size to increase capacity as more users joined the network, eventually transitioning most users to "thin" clients that don't store the (eventually enormous) complete blockchain.
The Core devs right now feel that the current situation (every node a full peer with the complete chain, but maxed out capacity and limited throughput) is preferable for a number of reasons including decentralization, while the Unlimited devs feel that it's time to increase the block size in order to increase capacity and get more users on the network, among other things.
Decisions like this are usually decided by the miner network reaching consensus, with votes counted through hashing power/mined blocks. I'm not sure where things stand at the moment, but it's been interesting to observe.
I understand it's become a rather contentious topic in the community.
IIUC, segwit makes certain kinds of complicated transactions easier to handle (ones with lots of inputs/outputs), possibly allowing more transactions to fit in less space, and lays useful groundwork for overlay networks like Lightning. I think the thinking is that overlay networks can be fast, and eventualy reconcile against the slower bitcoin network.
Unlimited would rather just scale up the bitcoin network in place, instead of relying on an overlay network.
You'd probably get better information from bitcoincore.org and bitcoinunlimited.info, or the subreddits /r/bitcoin and /r/btc (for core and unlimited, respectively, they split after moderator shenanigans in /r/bitcoin).
