I saw the single cluster and multi-way cluster quite a bit in some finance papers (cluster for standard error). I am asking for some simple explanation about what is cluster and why we need to do cluster (for single and multi-way cluster).
I saw a simple description here
Clustering of errors is technique to control for heteroskedasticity and autocorrelation. xtreg only allows for one way clustering, so for example in regression of academic outcomes of pupils on some education policy you could cluster on school level which would allow for heteroskedasticity of errors within cluster. Multi-way clustering allows you to add additional layers to those cluster, so you could maybe additionally cluster on county level or by year etc.
For example, why we need to cluster by school (single cluster) and why we need to do multi-way cluster (cluster by school and year)
Apart from that, I do not understand what does heteroskedasticity and autocorrelation mentioned above mean thoroughly.