A blockchain is composed of blocks each of which is attached to the previous block by adding the hash of the previous block in the current and the current hash in the block after and henceforth. Theses blocks that are attached to one and other in the blockchain are composed of transactions assembled by miners.
A blockchain is said to be immutable or a transaction is said to be immutable when included within the blockchain because upon insertion into the blockchain, the whole blockchain network(Miners) would have a copy of the ledger(Block) inclusive of the transaction. Guarantee against this sense of immutability is provided when the amount of computational power required to modify a transaction included within the blockchain is immensely huge that makes it impractical for anyone to establish malpractice as such.
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 majority of the source code implemented in Bitcoin protocol are open source meaning that anybody has all the right to go through, inspect 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 it essentially depends on the protocols and standards with which they are done that decide if it is indeed processed or not.
In all fairness, Consensus, mutual agreement between members of the Bitcoin community makes the Bitcoin economy so trustworthy.