How to get an array of file names

Question

I need a script for build an array with the names of files in a folder. For example in the folder1 I have 4 files, so the array must have in position 0,1,2,3 the names of these 4 files. I've found this script:

declare -a FILELIST
for f in *; do
     FILELIST[${#FILELIST[@]}+1]=$(echo "$f");
done

echo ${FILELIST[@]}                     

but I'm new to bash and I don't understand the meaning behind these commands.