Bit is a common unit used to designate a sub-unit of a bitcoin - 1,000,000 bits is equal to 1 bitcoin (BTC).
The UTXO set is the collection of all bitcoin addresses with unspent outputs.
A sidechain is a designation for a blockchain ledger that runs in parallel to a primary blockchain. Entries from the primary blockchain (where said entries typically represent digital assets) can be linked to and from the sidechain; this allows the sidechain to otherwise operate independently of the primary blockchain (e.g., by using an alternate means of record keeping, alternate consensus algorithm, etc.).
In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm that was described by Claus Schnorr. It is a digital signature scheme known for its simplicity, among the first whose security is based on the intractability of certain discrete logarithm problems. It is efficient and generates short signatures.
A seed phrase, seed recovery phrase or backup seed phrase is a list of words which store all the information needed to recover Bitcoin funds on-chain. Wallet software will typically generate a seed phrase and instruct the user to write it down on paper. If the user's computer breaks or their hard drive becomes corrupted, they can download the same wallet software again and use the paper backup to get their bitcoins back.
Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner. The generation of such keys depends on cryptographic algorithms based on mathematical problems to produce one-way functions. Effective security only requires keeping the private key private; the public key can be openly distributed without compromising security. In such a system, any person can encrypt a message using the receiver's public key, but that encrypted message can only be decrypted with the receiver's private key.
A transaction is a transfer of Bitcoin value that is broadcast to the network and collected into blocks. A transaction typically references previous transaction outputs as new transaction inputs and dedicates all input Bitcoin values to new outputs. Transactions are not encrypted, so it is possible to browse and view every transaction ever collected into a block. Once transactions are buried under enough confirmations they can be considered irreversible. Standard transaction outputs nominate addresses, and the redemption of any future inputs requires a relevant signature. All transactions are visible in the block chain, and can be viewed with a hex editor. A block chain browser is a site where every transaction included within the block chain can be viewed in human-readable terms. This is useful for seeing the technical details of transactions in action and for verifying payments.
An off-chain transaction is the movement of value outside of the block chain. A new block is added to the chain at random intervals averaging, by design, ten minutes (proof-of-work causes this delay). Together with the limit on block-size, this limits the number of transactions that can be processed in a given time. Some sites work around this problem using "off-chain payments" conducting transactions without writing them to the blockchain, which involves various trade offs regarding trust and transaction finality.
As Bitcoin has become more popular, the limit began to slow down transactions. A block is added to the chain every ten minutes. With a limit on its size, only so many transactions can be added, as many as fit in a block. Globally, bitcoin cannot currently support transactions with anything like the speed of other currencies or credit cards. It sometimes takes hours to confirm a transaction. Some sites work around this problem, by conducting "off-chain payments", conducting transactions without waiting for confirmation by the blockchain.
Once a new node joins the network, its first order of business is to download and validate the entire blockchain. This is an integral step to the distributed nature of bitcoin because only by doing this can a node claim that it has independently validated all transactions. As the blockchain grows in size, the time required for IBD increases unless optimizations are made to the code.