It's a trick that increases the block size without breaking backwards compatibility with non-Segwit nodes. I found this article by Jimmy Song to be more helpful than trying to understand the BIP.
The Segwit blocks are restricted by something called Block Weight. Block Weight is a new concept introduced in Segwit, and it’s calculated on a per-transaction basis. Each transaction has a “weight” which is defined this way:
(tx size with witness data stripped) * 3 + (tx size)
Non-Segwit transactions have zero witness data, so the weight for a non-Segwit transaction is exactly 4 times the size. Segwit transactions have some witness data so the weight is going to be less than 4 times the size. Note Segwit transactions are transmitted to Legacy nodes without witness data, so this formula will always result in blocks communicated to Legacy Nodes that are less than or equal to 1,000,000 bytes.
If you fill a block with non-Segwit transactions (0 bytes of witness data), the number of weight units (WU) will be calculated as
(1,000,000 B - 0 B) * 3 + 1,000,000 B = 4,000,000 WU
But the size of the block is still 1,000,000 bytes. This also means that you can fill a block with Segwit transactions, as long as their size, excluding the witness data, totals to 1,000,000 bytes or less. The reason this works is that non-Segwit nodes don't see the witness data for Segwit transactions, therefore they don't count it towards the block size.
As of 2018-01-21, there have been several blocks, such as this one, mined that are greater than 1MB.