How are new coins created, and why does the first transaction in a block matter?

The first transaction in each block mints new coins to whoever created the block (the "coinbase") — this rewards miners and distributes currency with no central issuer.

There is no authority to issue coins, so issuance is baked into mining: by convention the block's opening transaction pays fresh coins to the block's creator. The steady addition of new coins is analogous to gold miners expending resources to add gold to circulation — except here the resource spent is CPU time and electricity.

It serves two jobs at once: incentivising nodes to secure the network, and bootstrapping the initial distribution of coins.

Go deeper:

• Bitcoin — Wikipedia — how issuance is baked into mining, with no central issuer, and the gold-mining analogy.