A blockchain is composed of blocks, each of which is attached to the previous block. Blocks are attached by adding the hash of the previous block in the current and the current hash in the block after and henceforth. These blocks that are attached to one another in the blockchain are composed of transactions assembled by miners.
A blockchain or transaction is said to be immutable because upon insertion into the blockchain, the whole blockchain network of miners would have a copy of the block ledger, which is unique to the transaction, and includes information about each transaction within the blockchain. Guarantee against this sense of immutability happens when the amount of computational power required to modify a transaction is so immensely huge that makes it impractical for anyone to engage in malpractice.
Lack of dishonest practices and the sense of immutability contributes a massive amount of trust towards this project.
On a lighter note, one might ask, What makes democracy so trustworthy?
Yet, we can observe how democracy is seen as a wiser choice against centralized power.
It is also quite well known that the programs for mining and the majority of the source code implemented in Bitcoin protocol are open source, meaning that anybody has the right to go through, inspect it and modify the source code.
Bitcoin is only as powerful as its community for anything foreign and with the wrong intention is discarded and not used.
There have been instances where people have tried to embed malware and their success essentially depends on the protocols and standards with which they try to embed the malware that decides if it is indeed processed or not.
In all fairness, consensus and mutual agreement between members of the Bitcoin community make the Bitcoin economy so trustworthy.