Here's the problem the z/t value is supposed to help solve and an intuitive explanation how it does it. I'm going to gloss over a lot of extra complexities to try and keep things simple.
You drew a SAMPLE of $n$ rodents from a larger population of some large size (it doesn't matter how big the population itself is). Within this sample you estimate the mean of some value as $\bar{x}$ with a standard deviation of $\sigma$. You want to know if this estimate $\bar{x}$ is different from some known value $\mu$.
$\bar{x}$ and $\mu$ LOOK different but maybe, because you only only drew a sample of $n$ rodents, you got unluckily and just happened to estimate a value for $\bar{x}$ that is larger or smaller than $\mu$, even though, in reality the true value for ${x}$ in the population really is $\mu$.
To figure this out you calculate either a z value (if your n is "large," say > 30) or a t value (if it's < 30 or so). What does this value tell you? Well, we know from the central limit theorem that the errors associated with random sampling (that is - the extent to which an estimate from a sample will deviate from the true value in the population) follow a normal ("z") curve when the sample size is large, and a t curve when the sample size is small. In other words, if we drew a zillion different samples of size n and estimated $\bar{x}$ in each, the distribution of these estimates would form a normal/t curve around the true value ${x}$. How does this help us?
Let's start by assuming that the true value for ${x}$ in the population really is $\mu$. Then let's draw a z or t curve around $\mu$. That curve falls away as we get further away from $\mu$, indicating that, if ${x}$ really was equal to $\mu$ it would be less and less likely for us to have gotten unluckily enough to have estimated a value for $\bar{x}$ that was that far away from $\mu$.
In essence the z or t value tells you the number of standard deviations that your estimated value $\bar{x}$ is from $\mu$ on the appropriate z or t curve. So the bigger the t/ or z value, the less likely it is that $\bar{x}$ is actually $\mu$ and the more likely it is that they are different. By calculating the area under the z or t curve up to the z/t value (this is something we usually ask a computer to do) we actually estimated we can precisely estimate HOW unlikely (this is what's called a p value). So if we got a z value of 1.96 (around 2 standard deviations away) this means that, if $\bar{x}$ really were exactly equal to $\mu$ and we drew a zillion different size n samples from this same population, in less than 5% (p<.05) of them would we have gotten an estimate of $\bar{x}$ that is as far away from $\mu$ as we observe in the data we actually collected. Thus, as long as our samples really were random, we can be pretty confident that our estimated value $\bar{x}$ probably IS different from $\mu$.
