Jito Fees
The Jito Tip system was developed due to address certain shortcomings of the Solana transaction system:
Transactions are atomic (all transaction instructions must succeed for any of them to succeed), but there's a limit on how many instructions you can put in a transaction. If you make multiple transactions, some can succeed and others can fail.
On top of the above, the transactions can be split into an unexpected order, or even different blocks, causing unexpected behavior.
Very complex transactions can hit the compute limit per transaction (1.4 million CU) if they contain multiple complex instructions.
Calculating priority fees is a bit of a pain, it's a bit simpler with Jito Tip.
Jito Tip is a program that addresses these issues by allowing up to 5 transactions to be 'bundled' together. It will ensure that they will be executed sequentially, in the same block, and either all succeed or all fail. In other words, all 5 transactions are atomic. If any one transaction fails, none of them are committed to the blockchain. Fees are paid to one of only a few accounts, making fee estimation easier.
An important limitation of the Jito Tip program is that the validator processing the transactions must be running the Jito validator client. However, nearly all the validators on Solana do this.
Costs
As you might guess from the name, Jito Tip is not a free service. It requires paying a fee, to provide incentive for the validator to process your batch of up to 5 transactions before any other transactions. This fee is paid as a transfer instruction that sends SOL to one of several Jito Tip accounts -- this transfer instruction must be contained in a transaction in your batch. Often, its added as an instruction in the last transaction of a bundle.
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