Bitcoin core currently has a 1MB hard-limit, which limited the number of transactions that can be fitted into a block and transaction speed to approximately 7 transactions per second
What is it?
Segregated Witness, or SegWit is where signatures (which account for over 50% of the transaction)are removed from Bitcoin transactions. These transactions becomes smaller in size, freeing up each blocks for more transactions to be included. As the signatures are no longer counted, the 1MB limit essentially ballooned into 4MB.
Segwit attempts to strip off the signature and move it towards the end of the structure, increasing the number of transactions that can be fitted into a block.
TXID: Transaction ID
Why Not Increase Block Size?
Increasing the block size would essentially cause a hard fork since the new fork would no longer comply and conform to the old blocks. A hard fork requires everyone on the network to agree to upgrade to the new block size. Resistance towards SegWit led to the creation of Bitcoin Cash, a hard fork which increased the block size to a 8MB hard-limit.
SegWit is a soft fork, requiring miners to mine the SegWit-activated blocks without the need to update their software.
SegWit requires 95% consensus (hashpower) for it to be activated. As of June 2018, SegWit transactions exceeded 40%.
Imagine depositing checks into a box that has a maximum capacity of 1000 checks. With the activation of Segregated Witness, the check is cut into a quarter of the size, with only the necessary data (name of the parties and the numbers involved) on the front of the page and other information (signature) on the back. Each box can now hold 4000 checks.