Fitting input data into Gaussian distribution

I’m currently reading papers on Variational Autoencoders (VAE). According to this article (http://proceedings.mlr.press/v95/guo18a/guo18a.pdf):

By fitting the input data sample x(i) into the Gaussian distribution
with the reconstructed mean vector and the reconstructed standard
deviation vector, we can get the corresponding reconstruction
probability N (x(i)|µxˆ(i, l), σxˆ(i, l)) of the lth generated latent
vector.

Basically, I don’t understand what "fitting the input data sample x(i) into the Gaussian distribution" means. I assume we first build a Multivariate Gaussian distribution with the vectors µxˆ(i, l) and σxˆ(i, l). But then, what does that mean to fit a vector into that distribution?

Also, does the result of that calculation correspond to what we call the likelihood then?

Many thanks,

Guillaume