An ASIC-resistant cryptocurrency has its protocol and mining algorithm configured in such a way that using ASIC machines to mine the coin is either impossible or brings no significant benefit when compared to traditional GPU mining. In some cases, using ASICs on ASIC-resistant cryptocurrencies may be even worse than using the more conventional hardware.
Since mining involves multiple attempts of finding a solution for a sort of mathematical problem, the job of an ASIC is to perform as many attempts as possible (i.e., as many hashing functions per second as possible). This means that using ASICs to mine Bitcoin or other Proof of Work cryptocurrencies is much better than using a general-purpose piece of hardware, such as a GPU card.
However, the process of making a cryptocurrency ASIC-resistant is a defensive game, which requires continued development and modifications. This is due to the reason that ASIC designers and manufacturers are constantly producing new models of ASIC miners, and sometimes, the newer models are able to bypass the ASIC-resistance of certain cryptocurrencies.