The reparameterization trick is a technique used in Variational Autoencoders (VAEs) to enable the backpropagation algorithm to be applied to the model. It involves decoupling the stochastic part of the VAE's latent representation from the deterministic part. By introducing a separate noise variable, usually drawn from a standard normal distribution, the latent variables can be obtained as a deterministic function of this noise variable and other learnable parameters. This allows for the computation of gradients and enables the use of gradient-based optimization methods to train the VAE effectively.

The reparameterization trick is crucial in VAEs because it enables us to optimize the model's encoder and decoder networks using gradient-based methods. Without this trick, the gradients would not be able to flow through the random sampling process during the training phase, making it challenging to optimize the model effectively. By introducing the reparameterization trick, we ensure that the randomness in generating latent variables does not interfere with the training process.