Welcome!
Arguably the innovation of Bitcoin is to let one entry a community permitting to retailer and switch worth with little or no belief concerned. A consumer can obtain a publicly auditable software program (full node) and replay the state of the community since its inception, validating each single transition. This provides them certainty in regards to the validity of their transactions.
That is the motivation to run a full node. The flexibility to confirm the validity of (a set of) transaction(s) for your self as a substitute of asking a 3rd get together. That is additionally why a full node is commonly paired with a pockets, since on the whole the transactions you have an interest in validating are those concerned with the cash you obtain (instantly or not directly).
Now with regard to “validating a miner’s work”. In Bitcoin miners order transactions by together with them into blocks. Nodes obtain blocks from miners and validate them, typically partially. The quantity of validation carried out on acquired blocks decide how “full” a node is, kind of. The Bitcoin Core software program you downloaded for example verify that each one transactions are legitimate (no cash are stolen or created out of skinny air, the miner is not overpaying itself, and many others..) along with validating the miner’s proof-of-work.
Ensuring your full node is engaged on validating transactions might be the toughest half. It isn’t particular to Bitcoin, it’s simply on the whole exhausting for a consumer to confirm a software program does what it says on the tin. The Bitcoin Core growth workforce has been engaged on making this verification as accessible as attainable through the use of reproducible (and bootstrappable) builds for its releases in addition to following a public and documented growth course of (along with its code being Open Supply, in fact). The previous makes it attainable to confirm the binary software program you run in your pc really corresponds to a particular supply code, whereas the latter makes the life of somebody auditing the supply code a bit simpler.
In conclusion, the proposition of worth of Bitcoin is an open, accessible transaction system. A full node is probably the most belief minimized solution to entry this technique. It validates all info it receives (principally from miners, however usually not solely) to keep away from delegating this validation to a 3rd get together. There’s nonetheless some belief concerned within the software program performing the validation itself, there’s methods of mitigating this belief by making the verification of the software program extra accessible.